{"id":"https://openalex.org/W7207547390","doi":"https://doi.org/10.48550/arxiv.2609.02464","title":"When does propagation of chaos in the critical Curie-Weiss model stop?","display_name":"When does propagation of chaos in the critical Curie-Weiss model stop?","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7207547390","doi":"https://doi.org/10.48550/arxiv.2609.02464"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.02464","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02464","pdf_url":"https://arxiv.org/pdf/2609.02464","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/2609.02464","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028049323","display_name":"Nina Gantert","orcid":"https://orcid.org/0000-0003-0811-3651","observed_orcids":["https://orcid.org/0000-0003-0811-3651"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gantert, Nina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125965688","display_name":"Matthias L\u00f6we","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L\u00f6we, Matthias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5149486045","display_name":"Kilian Schnappinger","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schnappinger, Kilian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"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":0.8871999979019165,"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":0.8871999979019165,"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":0.08139999955892563,"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/T11716","display_name":"Random Matrices and Applications","score":0.007199999876320362,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/propagation-of-chaos","display_name":"propagation of chaos","score":0.9959999918937683},{"id":"https://openalex.org/keywords/mean-field-ising-model","display_name":"mean-field Ising model","score":0.9980000257492065},{"id":"https://openalex.org/keywords/critical-inverse-temperature","display_name":"critical inverse temperature","score":0.7730000019073486},{"id":"https://openalex.org/keywords/total-variation-distance","display_name":"total variation distance","score":0.8130000233650208},{"id":"https://openalex.org/keywords/product-measures","display_name":"product measures","score":0.421999990940094},{"id":"https://openalex.org/keywords/unimodality","display_name":"unimodality","score":0.781000018119812},{"id":"https://openalex.org/keywords/thermodynamic-limit","display_name":"thermodynamic limit","score":0.6100000143051147},{"id":"https://openalex.org/keywords/spin-glass","display_name":"spin glass","score":0.3199999928474426}],"concepts":[{"id":"https://openalex.org/C2778870898","wikidata":"https://www.wikidata.org/wiki/Q7577658","display_name":"Spins","level":2,"score":0.7702999711036682},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5335999727249146},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.5052000284194946},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.47589999437332153},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.47130000591278076},{"id":"https://openalex.org/C150775274","wikidata":"https://www.wikidata.org/wiki/Q1490646","display_name":"Spin glass","level":2,"score":0.4235999882221222},{"id":"https://openalex.org/C152401794","wikidata":"https://www.wikidata.org/wiki/Q583760","display_name":"Antisymmetric relation","level":2,"score":0.42160001397132874},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.42149999737739563},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.4129999876022339},{"id":"https://openalex.org/C2779374083","wikidata":"https://www.wikidata.org/wiki/Q5011038","display_name":"CHAOS (operating system)","level":2,"score":0.4058000147342682},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.38749998807907104},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.3855000138282776},{"id":"https://openalex.org/C21596040","wikidata":"https://www.wikidata.org/wiki/Q2896771","display_name":"Unimodality","level":2,"score":0.3813999891281128},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.36230000853538513},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3411000072956085},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.33820000290870667},{"id":"https://openalex.org/C42704618","wikidata":"https://www.wikidata.org/wiki/Q910917","display_name":"Spin (aerodynamics)","level":2,"score":0.33649998903274536},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C186603090","wikidata":"https://www.wikidata.org/wiki/Q55505926","display_name":"Distribution function","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2928999960422516},{"id":"https://openalex.org/C202759130","wikidata":"https://www.wikidata.org/wiki/Q7662148","display_name":"Synchronization of chaos","level":4,"score":0.2775000035762787},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C177562468","wikidata":"https://www.wikidata.org/wiki/Q182893","display_name":"Dispersion (optics)","level":2,"score":0.27219998836517334},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26460000872612},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.2556000053882599}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.02464","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02464","pdf_url":"https://arxiv.org/pdf/2609.02464","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.2609.02464","doi":"https://doi.org/10.48550/arxiv.2609.02464","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.02464","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:2609.02464","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02464","pdf_url":"https://arxiv.org/pdf/2609.02464","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/W7207547390.pdf","grobid_xml":"https://content.openalex.org/works/W7207547390.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4388700366","https://openalex.org/W4389364155","https://openalex.org/W7095953662","https://openalex.org/W2884311378","https://openalex.org/W4415968337","https://openalex.org/W7128835248","https://openalex.org/W2767049593","https://openalex.org/W2755366963","https://openalex.org/W6962997254","https://openalex.org/W4322832112"],"abstract_inverted_index":{"We":[0,26],"study":[1],"increasing":[2],"propagation":[3,47,62],"of":[4,36,39,48,58,63,69,99,102,113,118,127,141,144,147,157,160,163,176],"chaos":[5,49,64],"for":[6,34,56,92],"the":[7,13,61,76,93,100,103,110,125,128,132,138,145,148,154,158,161,167],"critical":[8,18],"Curie-":[9],"Weiss":[10],"model":[11,16],"(i.e.":[12],"mean-field":[14],"Ising":[15],"at":[17],"inverse":[19],"temperature":[20],"1,":[21],"with":[22,79,107],"no":[23],"external":[24],"field).":[25],"give":[27,88],"a":[28,70,116,151],"simple":[29],"way":[30],"to":[31,74,109,137],"see":[32,53],"that":[33],"windows":[35],"size":[37],"k(N)":[38,57,83,105,171],"smaller":[40],"order":[41,59],"than":[42],"sqrt{N}":[43,60],"we":[44,87],"still":[45],"have":[46],"(reproving":[50],"earlier":[51],"results,":[52],"e.g.[1]),":[54],"while":[55],"breaks":[65],"down.":[66],"The":[67],"law":[68,78,101,159],"single":[71],"spin":[72],"converges":[73],"\u03c0,":[75],"Bernoulli":[77],"parameter":[80],"1/2.":[81],"If":[82],"=":[84,170],"alpha":[85],"sqrt{N},":[86],"an":[89],"explicit":[90],"formula":[91],"limiting":[94],"distance":[95,136],"in":[96,131],"total":[97],"variation":[98],"first":[104,168],"spins":[106,129,165],"respect":[108],"k-fold":[111,139],"product":[112,140],"pi,":[114],"as":[115],"function":[117],"alpha.":[119],"For":[120],"even":[121],"larger":[122],"window":[123],"sizes,":[124],"distribution":[126],"has,":[130],"thermodynamical":[133],"limit,":[134],"maximal":[135],"pi.":[142],"One":[143],"ingredients":[146],"proof":[149],"is":[150],"result":[152],"about":[153],"unimodality/non-":[155],"unimodality":[156],"number":[162],"positive":[164],"among":[166],"k":[169],"spins,":[172],"which":[173],"may":[174],"be":[175],"independent":[177],"interest.":[178]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-04T00:00:00"}
