{"id":"https://openalex.org/W7204500141","doi":"https://doi.org/10.48550/arxiv.2608.24863","title":"Uniform logarithmic Sobolev inequalities for the 2D Coulomb gas at the diffusive temperature scale","display_name":"Uniform logarithmic Sobolev inequalities for the 2D Coulomb gas at the diffusive temperature scale","publication_year":2026,"publication_date":"2026-08-25","ids":{"openalex":"https://openalex.org/W7204500141","doi":"https://doi.org/10.48550/arxiv.2608.24863"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.24863","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24863","pdf_url":"https://arxiv.org/pdf/2608.24863","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/2608.24863","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017793144","display_name":"Matthew Rosenzweig","orcid":"https://orcid.org/0000-0001-8842-9263","observed_orcids":["https://orcid.org/0000-0001-8842-9263"]},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Rosenzweig, Matthew","raw_affiliation_strings":["Department of Mathematical Sciences , Carnegie Mellon University , 7127 Wean Hall , 5000 Forbes Avenue , Pittsburgh , PA 15213 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences , Carnegie Mellon University , 7127 Wean Hall , 5000 Forbes Avenue , Pittsburgh , PA 15213 , USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5017793144"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T11716","display_name":"Random Matrices and Applications","score":0.7910000085830688,"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"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.7910000085830688,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.06199999898672104,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.022299999371170998,"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/logarithmic-sobolev-inequality","display_name":"logarithmic Sobolev inequality","score":0.8679999709129333},{"id":"https://openalex.org/keywords/poincare-inequality","display_name":"Poincar\u00e9 inequality","score":0.9110000133514404},{"id":"https://openalex.org/keywords/canonical-ensemble","display_name":"canonical ensemble","score":0.6990000009536743},{"id":"https://openalex.org/keywords/gibbs-measures","display_name":"Gibbs measures","score":0.640999972820282},{"id":"https://openalex.org/keywords/conditional-entropy","display_name":"conditional entropy","score":0.5659999847412109},{"id":"https://openalex.org/keywords/dirichlet-forms","display_name":"Dirichlet forms","score":0.47699999809265137}],"concepts":[{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7748000025749207},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7728999853134155},{"id":"https://openalex.org/C185644265","wikidata":"https://www.wikidata.org/wiki/Q3711848","display_name":"Sobolev inequality","level":3,"score":0.6581000089645386},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.652999997138977},{"id":"https://openalex.org/C158444337","wikidata":"https://www.wikidata.org/wiki/Q2510435","display_name":"Gibbs measure","level":2,"score":0.5976999998092651},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4959000051021576},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4812999963760376},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4652999937534332},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4602000117301941},{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.43630000948905945},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4120999872684479},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3763999938964844},{"id":"https://openalex.org/C84498859","wikidata":"https://www.wikidata.org/wiki/Q5158327","display_name":"Concentration of measure","level":2,"score":0.3589000105857849},{"id":"https://openalex.org/C2777630202","wikidata":"https://www.wikidata.org/wiki/Q5527840","display_name":"Gaussian measure","level":3,"score":0.3474000096321106},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C118733216","wikidata":"https://www.wikidata.org/wiki/Q332504","display_name":"Absolute continuity","level":2,"score":0.30820000171661377},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.2948000133037567},{"id":"https://openalex.org/C9342510","wikidata":"https://www.wikidata.org/wiki/Q25406","display_name":"Coulomb","level":3,"score":0.27950000762939453},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.2782999873161316},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2703999876976013}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.24863","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24863","pdf_url":"https://arxiv.org/pdf/2608.24863","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.2608.24863","doi":"https://doi.org/10.48550/arxiv.2608.24863","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.24863","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:2608.24863","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.24863","pdf_url":"https://arxiv.org/pdf/2608.24863","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204500141.pdf","grobid_xml":"https://content.openalex.org/works/W7204500141.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W4402386030","https://openalex.org/W4403702927","https://openalex.org/W4403796773","https://openalex.org/W4416261061","https://openalex.org/W6891866094","https://openalex.org/W7162813435","https://openalex.org/W7203788094","https://openalex.org/W7203877786"],"related_works":["https://openalex.org/W2089329494","https://openalex.org/W2342659991","https://openalex.org/W2798525442","https://openalex.org/W83924355","https://openalex.org/W7155086238","https://openalex.org/W2262001819","https://openalex.org/W2789422235","https://openalex.org/W2090686942","https://openalex.org/W7097641381","https://openalex.org/W2047489998"],"abstract_inverted_index":{"For":[0],"$N\\ge2$":[1],"and":[2,65,97,122,132,148,184],"$\u03b2>0$,":[3],"consider":[4],"the":[5,25,89,93,98,103,108,112,162,169,195],"canonical":[6],"2D":[7],"Coulomb":[8],"gas":[9],"ensemble":[10],"\\begin{equation}":[11],"\\mathrm{d}\\mathbb{P}_{N,\u03b2}(Z)":[12],"=\\mathsf{Z}_{N,\u03b2}^{-1}e^{-\u03b2|Z|^2/2}":[13],"\\prod_{i0$,":[14],"this":[15],"Gibbs":[16],"measure":[17,96],"satisfies":[18],"a":[19,37,54,128,144,149,154],"logarithmic":[20,66,141,156,171],"Sobolev":[21,67,142,157,172],"inequality":[22,167],"(LSI)":[23],"on":[24,88,102,178],"closed":[26,181],"Dirichlet-form":[27],"domain":[28],"generated":[29],"by":[30,74,127,133],"collision-free":[31],"compactly":[32],"supported":[33],"smooth":[34],"functions,":[35],"with":[36,84,136,168],"positive":[38,78],"constant":[39,45],"independent":[40],"of":[41,57,77,80,92,107],"$N$.":[42],"The":[43,174],"LSI":[44],"may":[46],"be":[47],"chosen":[48],"uniformly":[49],"when":[50],"$\u03b2$":[51],"ranges":[52],"over":[53],"compact":[55],"subset":[56],"$(0,\\infty)$.":[58],"A":[59],"second":[60],"main":[61,176],"result":[62],"establishes":[63],"Poincar\u00e9":[64,115,166],"inequalities":[68],"for":[69],"planar":[70],"Gaussian":[71,95],"measures":[72],"weighted":[73,129],"finite":[75],"products":[76],"powers":[79],"distances":[81],"to":[82],"points,":[83],"constants":[85],"depending":[86],"only":[87],"total":[90,99],"variance":[91,119],"underlying":[94],"exponent,":[100],"not":[101],"number":[104],"or":[105],"locations":[106],"points.":[109],"To":[110],"prove":[111],"full":[113,164],"labeled":[114,165],"inequality,":[116,147],"we":[117],"decompose":[118],"into":[120],"permutation-invariant":[121],"label-dependent":[123],"parts,":[124],"controlled":[125],"respectively":[126],"$\\bar\\partial$":[130],"estimate":[131,152],"relative-coordinate":[134],"conditioning":[135],"random":[137],"transpositions;":[138],"separately,":[139],"one-site":[140],"inequalities,":[143],"conditional":[145],"entropy":[146],"repulsive":[150],"partition":[151],"give":[153],"defective":[155,170],"inequality.":[158,173],"Rothaus":[159],"tightening":[160],"combines":[161],"resulting":[163],"two":[175],"theorems":[177],"their":[179,189],"stated":[180],"form":[182],"domains":[183],"all":[185],"results":[186],"used":[187],"in":[188,200],"formal":[190],"proofs,":[191],"including":[192],"those":[193],"from":[194],"literature,":[196],"have":[197],"been":[198],"formalized":[199],"Lean":[201],"4.":[202]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-08-28T00:00:00"}
