{"id":"https://openalex.org/W7214052269","doi":"https://doi.org/10.48550/arxiv.2609.23994","title":"High-Dimensional Ultra-Log-Concave Distributions","display_name":"High-Dimensional Ultra-Log-Concave Distributions","publication_year":2026,"publication_date":"2026-09-21","ids":{"openalex":"https://openalex.org/W7214052269","doi":"https://doi.org/10.48550/arxiv.2609.23994"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.23994","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23994","pdf_url":"https://arxiv.org/pdf/2609.23994","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/2609.23994","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5020182392","display_name":"Zongchen Chen","orcid":"https://orcid.org/0009-0003-6112-2888","observed_orcids":["https://orcid.org/0009-0003-6112-2888"]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chen, Zongchen","raw_affiliation_strings":["School of Computer Science , Georgia Institute of Technology , Atlanta , GA , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science , Georgia Institute of Technology , Atlanta , GA , USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5152488815","display_name":"Sihan Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Sihan","raw_affiliation_strings":["Zhiyuan College , Shanghai Jiao Tong University , Shanghai , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhiyuan College , Shanghai Jiao Tong University , Shanghai , China","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.23929999768733978,"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"}},"topics":[{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.23929999768733978,"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"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.20839999616146088,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.19589999318122864,"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/weighted-poincare-inequality","display_name":"weighted Poincar\u00e9 inequality","score":0.902999997138977},{"id":"https://openalex.org/keywords/birth-death-chains","display_name":"birth-death chains","score":0.8790000081062317},{"id":"https://openalex.org/keywords/concentration-of-measure","display_name":"concentration of measure","score":0.9959999918937683},{"id":"https://openalex.org/keywords/maximum-entropy-principle","display_name":"maximum entropy principle","score":0.7639999985694885},{"id":"https://openalex.org/keywords/queueing-models","display_name":"queueing models","score":0.9020000100135803},{"id":"https://openalex.org/keywords/polymatroids","display_name":"polymatroids","score":0.9829999804496765},{"id":"https://openalex.org/keywords/antiferromagnetic-potts-model","display_name":"antiferromagnetic Potts model","score":0.9639999866485596}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7925999760627747},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5051000118255615},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48240000009536743},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4693000018596649},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4652000069618225},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4311999976634979},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4253999888896942},{"id":"https://openalex.org/C24084028","wikidata":"https://www.wikidata.org/wiki/Q7429781","display_name":"Scaling limit","level":3,"score":0.4032999873161316},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.39750000834465027},{"id":"https://openalex.org/C41054675","wikidata":"https://www.wikidata.org/wiki/Q185547","display_name":"Binomial distribution","level":2,"score":0.3953000009059906},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.3950999975204468},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.3741999864578247},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3695000112056732},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.3693999946117401},{"id":"https://openalex.org/C195579931","wikidata":"https://www.wikidata.org/wiki/Q3623548","display_name":"Applied probability","level":2,"score":0.3666999936103821},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3467000126838684},{"id":"https://openalex.org/C197096303","wikidata":"https://www.wikidata.org/wiki/Q869887","display_name":"Probability mass function","level":3,"score":0.34150001406669617},{"id":"https://openalex.org/C2781315470","wikidata":"https://www.wikidata.org/wiki/Q193623","display_name":"Binomial (polynomial)","level":2,"score":0.33869999647140503},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.33629998564720154},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.3334999978542328},{"id":"https://openalex.org/C55974624","wikidata":"https://www.wikidata.org/wiki/Q1188504","display_name":"Exponential family","level":2,"score":0.32690000534057617},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.32600000500679016},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C39947850","wikidata":"https://www.wikidata.org/wiki/Q729523","display_name":"Geometric distribution","level":3,"score":0.30550000071525574},{"id":"https://openalex.org/C99874945","wikidata":"https://www.wikidata.org/wiki/Q188715","display_name":"Statistical mechanics","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C130648207","wikidata":"https://www.wikidata.org/wiki/Q6007562","display_name":"Imprecise probability","level":3,"score":0.28870001435279846},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.2815999984741211},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2696000039577484},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C192065140","wikidata":"https://www.wikidata.org/wiki/Q1147928","display_name":"Multinomial distribution","level":2,"score":0.2596000134944916},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.2590999901294708},{"id":"https://openalex.org/C130359071","wikidata":"https://www.wikidata.org/wiki/Q5282057","display_name":"Discrete phase-type distribution","level":5,"score":0.25589999556541443},{"id":"https://openalex.org/C22684755","wikidata":"https://www.wikidata.org/wiki/Q847526","display_name":"Queueing theory","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.25360000133514404}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.23994","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23994","pdf_url":"https://arxiv.org/pdf/2609.23994","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.2609.23994","doi":"https://doi.org/10.48550/arxiv.2609.23994","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.23994","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:2609.23994","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.23994","pdf_url":"https://arxiv.org/pdf/2609.23994","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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214052269.pdf","grobid_xml":"https://content.openalex.org/works/W7214052269.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W4406186648","https://openalex.org/W4414971624","https://openalex.org/W4415315835","https://openalex.org/W4417287920","https://openalex.org/W4417431311","https://openalex.org/W7148877285","https://openalex.org/W7160125591","https://openalex.org/W7166562581","https://openalex.org/W7202137320","https://openalex.org/W7204204510","https://openalex.org/W7204461376"],"related_works":["https://openalex.org/W3157375027","https://openalex.org/W6979278024","https://openalex.org/W2109801194","https://openalex.org/W4407318699","https://openalex.org/W6910626323","https://openalex.org/W16649860","https://openalex.org/W2669398364","https://openalex.org/W1630297343","https://openalex.org/W2104796309","https://openalex.org/W2084623273"],"abstract_inverted_index":{"Ultra-log-concave":[0],"distributions":[1],"are":[2],"ubiquitous":[3],"in":[4,73],"probability,":[5],"combinatorics,":[6],"and":[7,10,56,65,95,135,142,152,166],"statistical":[8],"mechanics":[9],"have":[11],"been":[12],"studied":[13,47],"extensively.":[14],"In":[15],"this":[16,25,41],"paper,":[17],"we":[18],"introduce":[19],"a":[20,87,91,96,109,156],"quantitative":[21],"high-dimensional":[22],"extension":[23],"of":[24,123,131,160],"notion,":[26],"called":[27],"$\u03b4$-ultra-log-concavity,":[28],"for":[29,108,139,169],"probability":[30],"measures":[31],"on":[32],"$\\mathbb{N}^d$":[33],"with":[34,44,57,113],"downward":[35],"closed":[36],"support.":[37],"When":[38],"$\u03b4=":[39],"1$,":[40],"notion":[42],"coincides":[43],"the":[45,58,120,161],"class":[46,59],"by":[48,61],"Gurvits":[49],"(2009)":[50],"via":[51,68],"strongly":[52],"log-concave":[53,70],"generating":[54,71],"functions,":[55],"defined":[60],"Anari,":[62],"Oveis":[63],"Gharan,":[64],"Vinzant":[66],"(2021)":[67],"completely":[69],"functions;":[72],"one":[74],"dimension,":[75],"it":[76],"reduces":[77],"to":[78,145],"classical":[79],"ultra-log-concavity.":[80],"We":[81,127],"establish":[82,129],"several":[83,136],"functional":[84],"inequalities,":[85],"including":[86],"weighted":[88,97],"Poincar\u00e9":[89,165],"inequality,":[90,94],"discrete":[92,162],"Brascamp--Lieb":[93,167],"Wu-type":[98],"modified":[99],"log-Sobolev":[100],"inequality.":[101],"Our":[102],"approach":[103],"combines":[104],"integrated":[105],"Bakry--\u00c9mery":[106],"calculus":[107],"canonical":[110],"birth-death":[111],"chain":[112],"Poisson":[114],"stochastic":[115],"localization,":[116],"which":[117],"arises":[118],"as":[119],"time":[121],"reversal":[122],"coordinatewise":[124],"binomial":[125],"thinning.":[126],"further":[128],"concentration":[130],"measure,":[132],"maximum-entropy":[133],"principles,":[134],"closure":[137],"properties":[138],"ultra-log-concave":[140],"measures,":[141],"develop":[143],"applications":[144],"queueing":[146],"models,":[147,151],"polymatroids,":[148],"antiferromagnetic":[149],"Potts":[150],"hardcore":[153],"models.":[154],"Finally,":[155],"lattice":[157],"scaling":[158],"limit":[159],"theory":[163],"yields":[164],"inequalities":[168],"Laguerre":[170],"diffusions.":[171]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-23T00:00:00"}
