{"id":"https://openalex.org/W7204090401","doi":"https://doi.org/10.1214/26-aap2296","title":"On the first passage times of branching random walks in Rd","display_name":"On the first passage times of branching random walks in Rd","publication_year":2026,"publication_date":"2026-08-01","ids":{"openalex":"https://openalex.org/W7204090401","doi":"https://doi.org/10.1214/26-aap2296"},"language":"en","primary_location":{"id":"doi:10.1214/26-aap2296","doi":"https://doi.org/10.1214/26-aap2296","is_oa":false,"landing_page_url":"https://doi.org/10.1214/26-aap2296","pdf_url":null,"source":{"id":"https://openalex.org/S9093621","display_name":"The Annals of Applied Probability","issn_l":"1050-5164","issn":["1050-5164","2168-8737"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Applied Probability","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2404.09064","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011147039","display_name":"Jos\u00e9 Blanchet","orcid":"https://orcid.org/0000-0001-5895-0912","observed_orcids":["https://orcid.org/0000-0001-5895-0912"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jose Blanchet","raw_affiliation_strings":["Department of Management Science and Engineering, Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Management Science and Engineering, Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026754269","display_name":"Wei Cai A","orcid":"https://orcid.org/0000-0001-5919-8734","observed_orcids":["https://orcid.org/0000-0001-5919-8734","https://orcid.org/0000-0001-6590-2388"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wei Cai","raw_affiliation_strings":["Department of Mechanical Engineering, Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009063775","display_name":"Shaswat Mohanty","orcid":"https://orcid.org/0000-0001-6336-0001","observed_orcids":["https://orcid.org/0000-0001-6336-0001"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shaswat Mohanty","raw_affiliation_strings":["Department of Mechanical Engineering, Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5126851894","display_name":"Zhenyuan Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhenyuan Zhang","raw_affiliation_strings":["Department of Mathematics, Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Stanford University","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":5.2706,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.9335832,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"36","issue":"4","first_page":"3040","last_page":"3080"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":1.0,"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":1.0,"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/T13500","display_name":"Probability and Statistical Research","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11720","display_name":"Probability and Risk Models","score":0.0,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/branching-random-walk","display_name":"branching random walk","score":0.9240000247955322},{"id":"https://openalex.org/keywords/first-passage-time","display_name":"first passage time","score":0.9959999918937683},{"id":"https://openalex.org/keywords/asymptotic-analysis","display_name":"asymptotic analysis","score":0.6759999990463257},{"id":"https://openalex.org/keywords/logarithmic-corrections","display_name":"logarithmic corrections","score":0.8259999752044678},{"id":"https://openalex.org/keywords/tightness","display_name":"tightness","score":0.8579999804496765},{"id":"https://openalex.org/keywords/polymer-networks","display_name":"polymer networks","score":0.9110000133514404},{"id":"https://openalex.org/keywords/discrete-time-branching-processes","display_name":"discrete-time branching processes","score":0.6190000176429749}],"concepts":[{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.7477999925613403},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.722000002861023},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.4984999895095825},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.48890000581741333},{"id":"https://openalex.org/C2779806530","wikidata":"https://www.wikidata.org/wiki/Q4956437","display_name":"Branching random walk","level":3,"score":0.45590001344680786},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4553000032901764},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.4399000108242035},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.43560001254081726},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C154072304","wikidata":"https://www.wikidata.org/wiki/Q5747218","display_name":"Heterogeneous random walk in one dimension","level":3,"score":0.38940000534057617},{"id":"https://openalex.org/C206175624","wikidata":"https://www.wikidata.org/wiki/Q595731","display_name":"Branching (polymer chemistry)","level":2,"score":0.3817000091075897},{"id":"https://openalex.org/C186659197","wikidata":"https://www.wikidata.org/wiki/Q5452195","display_name":"First-hitting-time model","level":2,"score":0.3650999963283539},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.34209999442100525},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.29019999504089355},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2833000123500824},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.27900001406669617},{"id":"https://openalex.org/C177255742","wikidata":"https://www.wikidata.org/wiki/Q4109953","display_name":"Branching process","level":2,"score":0.2761000096797943},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C15964574","wikidata":"https://www.wikidata.org/wiki/Q7295534","display_name":"Rate function","level":3,"score":0.25600001215934753},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1214/26-aap2296","doi":"https://doi.org/10.1214/26-aap2296","is_oa":false,"landing_page_url":"https://doi.org/10.1214/26-aap2296","pdf_url":null,"source":{"id":"https://openalex.org/S9093621","display_name":"The Annals of Applied Probability","issn_l":"1050-5164","issn":["1050-5164","2168-8737"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","dongbi-b","doyens","jufo-3","norway-2","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319881","host_organization_name":"Institute of Mathematical Statistics","host_organization_lineage":["https://openalex.org/P4310319881"],"host_organization_lineage_names":["Institute of Mathematical Statistics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Annals of Applied Probability","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2404.09064","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2404.09064","pdf_url":"https://arxiv.org/pdf/2404.09064","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.2404.09064","doi":"https://doi.org/10.48550/arxiv.2404.09064","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2404.09064","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":"pmh:oai:arXiv.org:2404.09064","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2404.09064","pdf_url":"https://arxiv.org/pdf/2404.09064","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1189513000","display_name":"Robust Wasserstein Profile Inference","funder_award_id":"1915967","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1468320059","display_name":"DMS-EPSRC: Fast Martingales, Large Deviations, and Randomized Gradients for Heavy-tailed Distributions","funder_award_id":"2118199","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4650965343","display_name":"Collaborative Research: CIF: Medium: Statistical and Algorithmic Foundations of Distributionally Robust Policy Learning","funder_award_id":"2312204","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5658145429","display_name":"Collaborative Research: AMPS: Rare Events in Power Systems: Novel Mathematics, Statistics and Algorithms.","funder_award_id":"2229012","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204090401.pdf","grobid_xml":"https://content.openalex.org/works/W7204090401.grobid-xml"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W605936007","https://openalex.org/W1495091143","https://openalex.org/W1879525117","https://openalex.org/W1964096464","https://openalex.org/W1971797516","https://openalex.org/W1988640029","https://openalex.org/W1990295631","https://openalex.org/W2006851042","https://openalex.org/W2013261240","https://openalex.org/W2030234558","https://openalex.org/W2052469513","https://openalex.org/W2060952137","https://openalex.org/W2065232720","https://openalex.org/W2079949023","https://openalex.org/W2086030421","https://openalex.org/W2097649415","https://openalex.org/W2098130249","https://openalex.org/W2106730112","https://openalex.org/W2127129887","https://openalex.org/W2130847288","https://openalex.org/W2139310454","https://openalex.org/W2141240899","https://openalex.org/W2159477701","https://openalex.org/W2170579194","https://openalex.org/W2184066691","https://openalex.org/W2273740195","https://openalex.org/W2274062199","https://openalex.org/W2609926569","https://openalex.org/W2787800095","https://openalex.org/W2963035903","https://openalex.org/W2964138256","https://openalex.org/W3037050335","https://openalex.org/W3044473681","https://openalex.org/W3158285048","https://openalex.org/W3185974289","https://openalex.org/W4211192810","https://openalex.org/W4221164603","https://openalex.org/W4246761209","https://openalex.org/W4254010946","https://openalex.org/W4296840292","https://openalex.org/W4301258660","https://openalex.org/W4302324459","https://openalex.org/W4353080945","https://openalex.org/W4387030109","https://openalex.org/W4393971332","https://openalex.org/W4399771514","https://openalex.org/W4403928634","https://openalex.org/W4411750636","https://openalex.org/W4415880797","https://openalex.org/W4416565591","https://openalex.org/W7161801291"],"related_works":["https://openalex.org/W4394867673","https://openalex.org/W4403928634","https://openalex.org/W7196947975","https://openalex.org/W4415333476","https://openalex.org/W4416565591","https://openalex.org/W4387149075","https://openalex.org/W173371410","https://openalex.org/W2402164675","https://openalex.org/W2280475471","https://openalex.org/W2749967089"],"abstract_inverted_index":{"We":[0,26,50,101],"study":[1],"the":[2,16,19,30,45,53,58,95,107],"first":[3,31,98,108],"passage":[4,32,99,109],"times":[5,33],"of":[6,18,29,37,64,74,91,97,106],"discrete-time":[7],"branching":[8,115],"random":[9,116],"walks":[10],"in":[11,129],"Rd":[12],"where":[13],"d\u22651.":[14],"Here,":[15],"genealogy":[17],"particles":[20],"follows":[21],"a":[22,35,41,113],"supercritical":[23],"Galton\u2013Watson":[24],"process.":[25],"provide":[27,52],"asymptotics":[28,67],"to":[34,71,82,112,123],"ball":[36],"radius":[38],"one":[39],"at":[40],"distance":[42],"x":[43],"from":[44],"origin,":[46],"conditioned":[47],"upon":[48],"survival.":[49],"explicitly":[51],"linear":[54],"dominating":[55],"term":[56,61],"and":[57,80],"logarithmic":[59],"correction":[60],"as":[62],"functions":[63],"x.":[65],"The":[66],"are":[68],"precise":[69],"up":[70,81],"an":[72,104],"order":[73],"oP(logx)":[75],"for":[76,84],"general":[77],"jump":[78],"distributions":[79],"OP(loglogx)":[83],"spherically":[85],"symmetric":[86],"jumps.":[87],"A":[88],"crucial":[89],"ingredient":[90],"both":[92],"results":[93],"is":[94],"tightness":[96],"times.":[100],"also":[102],"discuss":[103],"extension":[105],"time":[110],"analysis":[111],"modified":[114],"walk":[117],"model":[118],"that":[119],"has":[120],"been":[121],"proven":[122],"successfully":[124],"capture":[125],"shortest":[126],"path":[127],"statistics":[128],"polymer":[130],"networks.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-25T00:00:00"}