{"id":"https://openalex.org/W7214389236","doi":"https://doi.org/10.48550/arxiv.2609.29671","title":"Dimer model and random lattice permutations with general weights","display_name":"Dimer model and random lattice permutations with general weights","publication_year":2026,"publication_date":"2026-08-30","ids":{"openalex":"https://openalex.org/W7214389236","doi":"https://doi.org/10.48550/arxiv.2609.29671"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.29671","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29671","pdf_url":"https://arxiv.org/pdf/2609.29671","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.29671","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5106276620","display_name":"Andreas Klippel","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I197323543","display_name":"Johannes Gutenberg University Mainz","ror":"https://ror.org/023b0x485","country_code":"DE","type":"education","lineage":["https://openalex.org/I197323543"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klippel, Andreas","raw_affiliation_strings":["Johannes Gutenberg-Universit\u00e4t Mainz , Institut f\u00fcr Mathematik , Mainz , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johannes Gutenberg-Universit\u00e4t Mainz , Institut f\u00fcr Mathematik , Mainz , Germany","institution_ids":["https://openalex.org/I197323543"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011864453","display_name":"Lorenzo Taggi","orcid":"https://orcid.org/0000-0002-7085-9764","observed_orcids":["https://orcid.org/0000-0002-7085-9764"]},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Taggi, Lorenzo","raw_affiliation_strings":["Sapienza Universit\u00e0 di Roma , Dipartimento di Matematica , Roma , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Sapienza Universit\u00e0 di Roma , Dipartimento di Matematica , Roma , Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5152864861","display_name":"Wei Wu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I258800397","display_name":"New York University Shanghai","ror":"https://ror.org/02vpsdb40","country_code":"CN","type":"education","lineage":["https://openalex.org/I258800397","https://openalex.org/I57206974"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wu, Wei","raw_affiliation_strings":["NYU Shanghai , Mathematics Department and NYU-ECNU Math Institute , Shanghai , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"NYU Shanghai , Mathematics Department and NYU-ECNU Math Institute , Shanghai , China","institution_ids":["https://openalex.org/I258800397"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9657999873161316,"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":0.9657999873161316,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.025499999523162842,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.002199999988079071,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dimer-model","display_name":"dimer model","score":0.996999979019165},{"id":"https://openalex.org/keywords/perfect-matchings","display_name":"perfect matchings","score":0.8799999952316284},{"id":"https://openalex.org/keywords/long-range-order","display_name":"long-range order","score":0.8349999785423279},{"id":"https://openalex.org/keywords/periodic-box","display_name":"periodic box","score":0.6069999933242798},{"id":"https://openalex.org/keywords/loop-configuration","display_name":"loop configuration","score":0.41100001335144043}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7656999826431274},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7322999835014343},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7005000114440918},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.6092000007629395},{"id":"https://openalex.org/C2779546866","wikidata":"https://www.wikidata.org/wiki/Q531306","display_name":"Dimer","level":2,"score":0.5146999955177307},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.5080999732017517},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5027999877929688},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.4065999984741211},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3619000017642975},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3472000062465668},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.30140000581741333},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2572999894618988},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.25189998745918274}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.29671","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29671","pdf_url":"https://arxiv.org/pdf/2609.29671","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.2609.29671","doi":"https://doi.org/10.48550/arxiv.2609.29671","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.29671","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.29671","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29671","pdf_url":"https://arxiv.org/pdf/2609.29671","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":[],"funders":[{"id":"https://openalex.org/F4320322510","display_name":"Sapienza Universit\u00e0 di Roma","ror":"https://ror.org/02be6w209"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214389236.pdf","grobid_xml":"https://content.openalex.org/works/W7214389236.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4366330696","https://openalex.org/W4401882268","https://openalex.org/W4415343305"],"related_works":["https://openalex.org/W7167792103","https://openalex.org/W6888496588","https://openalex.org/W3194800990","https://openalex.org/W2119740160","https://openalex.org/W1496085627","https://openalex.org/W1178680599","https://openalex.org/W2046521351","https://openalex.org/W4385588461","https://openalex.org/W2397619905","https://openalex.org/W2142554063"],"abstract_inverted_index":{"The":[0],"dimer":[1,37,53],"model":[2],"and":[3,17,52,102,115,124],"random":[4],"lattice":[5],"permutations":[6],"are":[7,55,72,79],"two":[8,62],"fundamental":[9],"objects":[10],"at":[11],"the":[12,36,67,82,103,142],"interface":[13],"of":[14,74,85,91,93,105,141],"probability,":[15],"combinatorics,":[16],"mathematical":[18],"physics.":[19],"We":[20,145],"study":[21],"these":[22,147],"models":[23],"on":[24,48],"finite":[25,94],"periodic":[26],"boxes":[27],"in":[28,128],"$\\mathbb":[29],"Z^d$":[30],"within":[31],"a":[32,44],"common":[33],"framework.":[34],"For":[35,88],"model,":[38,69],"edges":[39,114],"connecting":[40],"arbitrary":[41],"vertices":[42],"carry":[43],"weight":[45],"which":[46],"depends":[47],"their":[49,58,86],"relative":[50],"displacement":[51,84],"configurations":[54,71],"weighted":[56,80],"through":[57,81],"occupied":[59],"edges.":[60],"Superimposing":[61],"independent":[63],"perfect":[64],"matchings":[65],"gives":[66],"double-dimer":[68],"whose":[70],"collections":[73],"disjoint":[75],"loops.":[76,107],"Permutations,":[77],"instead,":[78],"spatial":[83],"jumps.":[87,116],"broad":[89],"classes":[90],"weights":[92,120],"or":[95],"infinite":[96],"range":[97],"we":[98],"prove":[99],"long-range":[100,119,122],"order":[101,123],"occurrence":[104],"macroscopic":[106,125],"This":[108],"extends":[109],"nearest-neighbour":[110,143],"results":[111,148],"to":[112],"arbitrary-range":[113],"In":[117,131],"particular,":[118],"yield":[121],"loops":[126],"already":[127],"dimensions":[129],"$d=1,2$.":[130],"dimension":[132],"two,":[133],"this":[134],"behaviour":[135],"is":[136],"qualitatively":[137],"different":[138],"from":[139],"that":[140],"model.":[144],"complement":[146],"with":[149],"sharp":[150],"absence":[151],"criteria.":[152]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-26T00:00:00"}
