{"id":"https://openalex.org/W4415112312","doi":"https://doi.org/10.1007/s00440-026-01516-7","title":"Permutation invariance in last-passage percolation and the distribution of the Busemann process","display_name":"Permutation invariance in last-passage percolation and the distribution of the Busemann process","publication_year":2026,"publication_date":"2026-07-22","ids":{"openalex":"https://openalex.org/W4415112312","doi":"https://doi.org/10.1007/s00440-026-01516-7","pmid":"https://pubmed.ncbi.nlm.nih.gov/42964467","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/13719824"},"language":"en","primary_location":{"id":"doi:10.1007/s00440-026-01516-7","doi":"https://doi.org/10.1007/s00440-026-01516-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00440-026-01516-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00440-026-01516-7.pdf","source":{"id":"https://openalex.org/S105693234","display_name":"Probability Theory and Related Fields","issn_l":"0178-8051","issn":["0178-8051","1432-2064"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Probability Theory and Related Fields","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00440-026-01516-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082281030","display_name":"Erik Bates","orcid":"https://orcid.org/0000-0002-3472-036X","observed_orcids":["https://orcid.org/0000-0002-3472-036X"]},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Erik Bates","raw_affiliation_strings":["Department of Mathematics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27695-8205 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, North Carolina State University, 2311 Stinson Drive, Raleigh, NC 27695-8205 USA","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004049378","display_name":"Elnur Emrah","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I100930933","display_name":"University College Dublin","ror":"https://ror.org/05m7pjf47","country_code":"IE","type":"education","lineage":["https://openalex.org/I100930933"]}],"countries":["IE"],"is_corresponding":false,"raw_author_name":"Elnur Emrah","raw_affiliation_strings":["School of Mathematics and Statistics, University College Dublin, Dublin, Ireland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University College Dublin, Dublin, Ireland","institution_ids":["https://openalex.org/I100930933"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103565314","display_name":"James Martin","orcid":"https://orcid.org/0009-0009-8935-6188","observed_orcids":["https://orcid.org/0009-0009-8935-6188"]},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"James Martin","raw_affiliation_strings":["Department of Statistics, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Oxford, 24-29 St Giles', Oxford, OX1 3LB UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024096400","display_name":"Timo Sepp\u00e4l\u00e4inen","orcid":"https://orcid.org/0000-0003-0683-8819","observed_orcids":["https://orcid.org/0000-0003-0683-8819"]},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Timo Sepp\u00e4l\u00e4inen","raw_affiliation_strings":["Mathematics Department, University of Wisconsin-Madison, Van Vleck Hall, 480 Lincoln Dr., Madison, WI 53706-1388 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, University of Wisconsin-Madison, Van Vleck Hall, 480 Lincoln Dr., Madison, WI 53706-1388 USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077685643","display_name":"Evan Sorensen","orcid":"https://orcid.org/0000-0003-2987-0889","observed_orcids":["https://orcid.org/0000-0003-2987-0889"]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Evan Sorensen","raw_affiliation_strings":["Department of Mathematics, Columbia University, Room 624, MC 4432, 2990 Broadway, New York, NY 10027 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Columbia University, Room 624, MC 4432, 2990 Broadway, New York, NY 10027 USA","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5082281030"],"corresponding_institution_ids":["https://openalex.org/I137902535"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":{"value":3090,"currency":"USD","value_usd":3090},"fwci":9.1387,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.97943287,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"196","issue":"5-6","first_page":"2609","last_page":"2674"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.00039999998989515007,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/last-passage-percolation","display_name":"last passage percolation","score":0.9950000047683716},{"id":"https://openalex.org/keywords/busemann-functions","display_name":"Busemann functions","score":0.9330000281333923},{"id":"https://openalex.org/keywords/permutation-invariance","display_name":"permutation invariance","score":0.9549999833106995},{"id":"https://openalex.org/keywords/joint-probability-distribution","display_name":"joint probability distribution","score":0.722000002861023},{"id":"https://openalex.org/keywords/rsk-correspondence","display_name":"RSK correspondence","score":0.8579999804496765}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7135999798774719},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.6927000284194946},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6292999982833862},{"id":"https://openalex.org/C18555067","wikidata":"https://www.wikidata.org/wiki/Q8375051","display_name":"Joint (building)","level":2,"score":0.6194999814033508},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5820000171661377},{"id":"https://openalex.org/C200985842","wikidata":"https://www.wikidata.org/wiki/Q3375503","display_name":"Random permutation","level":3,"score":0.4587000012397766},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4401000142097473},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.43810001015663147},{"id":"https://openalex.org/C165216359","wikidata":"https://www.wikidata.org/wiki/Q670653","display_name":"Marginal distribution","level":3,"score":0.43779999017715454},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.4269999861717224},{"id":"https://openalex.org/C2780457167","wikidata":"https://www.wikidata.org/wiki/Q17156484","display_name":"Percolation (cognitive psychology)","level":2,"score":0.4242999851703644},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4023999869823456},{"id":"https://openalex.org/C65778772","wikidata":"https://www.wikidata.org/wiki/Q12345341","display_name":"Asymptotic distribution","level":3,"score":0.3869999945163727},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.3653999865055084},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36090001463890076},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.3580000102519989},{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3366999924182892},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.31940001249313354},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.3102000057697296},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.30090001225471497},{"id":"https://openalex.org/C102094743","wikidata":"https://www.wikidata.org/wiki/Q133871","display_name":"Normal distribution","level":2,"score":0.3000999987125397},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.2957000136375427},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2892000079154968},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2831999957561493},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.2750000059604645},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.273499995470047},{"id":"https://openalex.org/C98184364","wikidata":"https://www.wikidata.org/wiki/Q1780131","display_name":"Argument (complex analysis)","level":2,"score":0.2574000060558319},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2554999887943268},{"id":"https://openalex.org/C60775368","wikidata":"https://www.wikidata.org/wiki/Q17099337","display_name":"Natural exponential family","level":3,"score":0.25099998712539673}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00440-026-01516-7","doi":"https://doi.org/10.1007/s00440-026-01516-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00440-026-01516-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00440-026-01516-7.pdf","source":{"id":"https://openalex.org/S105693234","display_name":"Probability Theory and Related Fields","issn_l":"0178-8051","issn":["0178-8051","1432-2064"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Probability Theory and Related Fields","raw_type":"journal-article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13719824","doi":null,"is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13719824/","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13719824/pdf/440_2026_Article_1516.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Probab Theory Relat Fields","raw_type":"Text"},{"id":"pmid:42964467","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42964467","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Probability theory and related fields","raw_type":"Journal Article"},{"id":"pmh:oai:arXiv.org:2506.12641","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2506.12641","pdf_url":"https://arxiv.org/pdf/2506.12641","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2506.12641","doi":"https://doi.org/10.48550/arxiv.2506.12641","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2506.12641","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1007/s00440-026-01516-7","doi":"https://doi.org/10.1007/s00440-026-01516-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00440-026-01516-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00440-026-01516-7.pdf","source":{"id":"https://openalex.org/S105693234","display_name":"Probability Theory and Related Fields","issn_l":"0178-8051","issn":["0178-8051","1432-2064"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a-star","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Probability Theory and Related Fields","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G376356821","display_name":"Structure and Statistics of Disordered Systems","funder_award_id":"2412473","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3916375613","display_name":"Growth and Motion in a Random Medium","funder_award_id":"2152362","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6277018575","display_name":"Growth and Motion in a Random Medium","funder_award_id":"2448375","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6863674734","display_name":"Particle systems, growth models and their probabilistic structures","funder_award_id":"EP/W032112/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7947662707","display_name":null,"funder_award_id":"1019133","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"},{"id":"https://openalex.org/F4320306555","display_name":"Wisconsin Alumni Research Foundation","ror":"https://ror.org/00hwxbz16"},{"id":"https://openalex.org/F4320318630","display_name":"Irish Research eLibrary","ror":"https://ror.org/05c347015"},{"id":"https://openalex.org/F4320320290","display_name":"University of Oxford","ror":"https://ror.org/052gg0110"},{"id":"https://openalex.org/F4320320360","display_name":"University of Bristol","ror":"https://ror.org/0524sp257"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415112312.pdf","grobid_xml":"https://content.openalex.org/works/W4415112312.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W53136209","https://openalex.org/W73817974","https://openalex.org/W1552186532","https://openalex.org/W1552894041","https://openalex.org/W1792163857","https://openalex.org/W1969051672","https://openalex.org/W1988878343","https://openalex.org/W1994412729","https://openalex.org/W2015533295","https://openalex.org/W2016850222","https://openalex.org/W2025386901","https://openalex.org/W2037872680","https://openalex.org/W2047493173","https://openalex.org/W2066459155","https://openalex.org/W2075303759","https://openalex.org/W2080484553","https://openalex.org/W2086255021","https://openalex.org/W2086952222","https://openalex.org/W2087504203","https://openalex.org/W2118752646","https://openalex.org/W2123829630","https://openalex.org/W2127825100","https://openalex.org/W2162315922","https://openalex.org/W2195063482","https://openalex.org/W2220946015","https://openalex.org/W2253529481","https://openalex.org/W2270537879","https://openalex.org/W2334297521","https://openalex.org/W2443786406","https://openalex.org/W2593145681","https://openalex.org/W2754930321","https://openalex.org/W2797645676","https://openalex.org/W2889497241","https://openalex.org/W2894793529","https://openalex.org/W2903509700","https://openalex.org/W2924210525","https://openalex.org/W2947965511","https://openalex.org/W2963432960","https://openalex.org/W2964345487","https://openalex.org/W2965314093","https://openalex.org/W2969926885","https://openalex.org/W2969957855","https://openalex.org/W2992574193","https://openalex.org/W2999074785","https://openalex.org/W3008463181","https://openalex.org/W3023386001","https://openalex.org/W3134979822","https://openalex.org/W3160850120","https://openalex.org/W3176326373","https://openalex.org/W4226113075","https://openalex.org/W4294287724","https://openalex.org/W4306767253","https://openalex.org/W4309130944","https://openalex.org/W4367679977","https://openalex.org/W4385381610","https://openalex.org/W4391363521","https://openalex.org/W4396601144","https://openalex.org/W4403556606","https://openalex.org/W4407879933","https://openalex.org/W4408006850","https://openalex.org/W4408865470","https://openalex.org/W4408925477","https://openalex.org/W4416420937"],"related_works":["https://openalex.org/W7202119649","https://openalex.org/W4385381610","https://openalex.org/W2113265009","https://openalex.org/W4416246558","https://openalex.org/W3134979822","https://openalex.org/W7098889602","https://openalex.org/W2945529483","https://openalex.org/W3207707635","https://openalex.org/W3172076088","https://openalex.org/W2964193541"],"abstract_inverted_index":{"Abstract":[0],"In":[1,148],"i.i.d.":[2],"exponential":[3],"last-passage":[4,26,62,185],"percolation,":[5],"we":[6,151],"describe":[7],"the":[8,35,99,113,145,149,158,167,190,196,207,212,222,227,230],"joint":[9,25,86,114,146,181],"distribution":[10,56,88,115],"of":[11,23,61,119,157,175,183,189,195,203,211,221,229],"Busemann":[12,36,87,160],"functions,":[13],"over":[14,18],"all":[15,19],"edges":[16,120],"and":[17,47,98,139,166,169,215,225],"directions,":[20,52],"in":[21,28,55],"terms":[22],"a":[24,29,39,58,65,93,124,179],"problem":[27],"finite":[30],"inhomogeneous":[31,159,184],"environment.":[32],"More":[33],"specifically,":[34],"increments":[37,63],"within":[38],"$$k\\times":[40],"\\ell":[41],"$$":[42],"k":[43,70],"\u00d7":[44,76],"\u2113":[45,78],"grid,":[46],"associated":[48],"to":[49,57,142,217],"d":[50,72,80],"different":[51,199],"are":[53],"equal":[54],"particular":[59],"collection":[60,118],"inside":[64],"$$(k+d-1)\\times":[66],"(\\ell":[67],"+d-1)$$":[68],"(":[69,77],"+":[71,79],"-":[73,81],"1":[74,82],")":[75,83],"grid.":[84],"The":[85,172],"was":[89],"previously":[90],"described":[91],"along":[92,123],"horizontal":[94,125],"line":[95],"by":[96,164],"Fan":[97],"fourth":[100,170],"author,":[101],"using":[102,127,206],"certain":[103],"queueing":[104],"maps.":[105],"By":[106],"contrast,":[107],"our":[108,176],"new":[109],"description":[110],"explicitly":[111],"gives":[112],"for":[116],"any":[117],"(not":[121],"just":[122],"line)":[126],"only":[128],"finitely":[129],"many":[130],"random":[131],"variables.":[132],"Our":[133,193],"result":[134],"thus":[135],"provides":[136],"an":[137,218],"exact":[138],"accessible":[140],"way":[141],"sample":[143],"from":[144,200],"distribution.":[147],"proof,":[150],"rely":[152],"on":[153],"one-directional":[154],"marginal":[155],"distributions":[156],"functions":[161],"recently":[162],"studied":[163],"Janjigian":[165],"second":[168,173],"authors.":[171],"ingredient":[174],"proof":[177,194],"is":[178,198],"novel":[180],"invariance":[182,197],"times":[186],"under":[187],"permutations":[188],"inhomogeneity":[191],"parameters.":[192,231],"earlier":[201],"proofs":[202],"such":[204],"results,":[205],"Burke":[208],"property":[209],"instead":[210],"RSK":[213],"correspondence,":[214],"leading":[216],"explicit":[219],"coupling":[220],"weights":[223],"before":[224],"after":[226],"permutation":[228]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2025-10-13T00:00:00"}
