{"id":"https://openalex.org/W7202416718","doi":"https://doi.org/10.48550/arxiv.2608.10515","title":"Limiting Law of Local Fields for the Mean Field Ghatak-Sherrington Model","display_name":"Limiting Law of Local Fields for the Mean Field Ghatak-Sherrington Model","publication_year":2026,"publication_date":"2026-08-11","ids":{"openalex":"https://openalex.org/W7202416718","doi":"https://doi.org/10.48550/arxiv.2608.10515"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.10515","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.10515","pdf_url":"https://arxiv.org/pdf/2608.10515","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":"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/2608.10515","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147104114","display_name":"Yunhui Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chen, Yunhui","raw_affiliation_strings":["School of Mathematics , University of Minnesota , 127 Vincent Hall 206 Church St. SE Min- neapolis , MN 55455"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , University of Minnesota , 127 Vincent Hall 206 Church St. SE Min- neapolis , MN 55455","institution_ids":["https://openalex.org/I130238516"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5147122560","display_name":"Keaton Fierro","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fierro, Keaton","raw_affiliation_strings":["School of Mathematics , University of Minnesota , 127 Vincent Hall 206 Church St. SE Min- neapolis , MN 55455"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics , University of Minnesota , 127 Vincent Hall 206 Church St. SE Min- neapolis , MN 55455","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I130238516"],"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/T11716","display_name":"Random Matrices and Applications","score":0.9429000020027161,"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":0.9429000020027161,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.015200000256299973,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.011900000274181366,"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/mean-field-spin-glasses","display_name":"mean-field spin glasses","score":0.7839999794960022},{"id":"https://openalex.org/keywords/central-limit-theorem","display_name":"central limit theorem","score":0.9160000085830688},{"id":"https://openalex.org/keywords/cavity-field","display_name":"cavity field","score":0.7580000162124634},{"id":"https://openalex.org/keywords/cavity-method","display_name":"cavity method","score":0.5920000076293945},{"id":"https://openalex.org/keywords/high-temperature-regime","display_name":"high temperature regime","score":0.8289999961853027},{"id":"https://openalex.org/keywords/method-of-moments","display_name":"method of moments","score":0.6589999794960022}],"concepts":[{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.659600019454956},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6060000061988831},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.551800012588501},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5188999772071838},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5095000267028809},{"id":"https://openalex.org/C84583765","wikidata":"https://www.wikidata.org/wiki/Q1868517","display_name":"Local field","level":2,"score":0.4860999882221222},{"id":"https://openalex.org/C166785042","wikidata":"https://www.wikidata.org/wiki/Q190391","display_name":"Central limit theorem","level":2,"score":0.48249998688697815},{"id":"https://openalex.org/C202213908","wikidata":"https://www.wikidata.org/wiki/Q626011","display_name":"Mean field theory","level":2,"score":0.4794999957084656},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.47429999709129333},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.45329999923706055},{"id":"https://openalex.org/C51267290","wikidata":"https://www.wikidata.org/wiki/Q5527848","display_name":"Gaussian random field","level":4,"score":0.385699987411499},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37599998712539673},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.3659000098705292},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.33889999985694885},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.33230000734329224},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.3206999897956848},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30399999022483826},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.2757999897003174},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.272599995136261}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.10515","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.10515","pdf_url":"https://arxiv.org/pdf/2608.10515","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.10515","doi":"https://doi.org/10.48550/arxiv.2608.10515","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.10515","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:2608.10515","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.10515","pdf_url":"https://arxiv.org/pdf/2608.10515","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":"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/W7202416718.pdf","grobid_xml":"https://content.openalex.org/works/W7202416718.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2155870649","https://openalex.org/W7095333899","https://openalex.org/W4403644426","https://openalex.org/W4402706394","https://openalex.org/W7100618770","https://openalex.org/W1964487177","https://openalex.org/W2039578875","https://openalex.org/W4403401736","https://openalex.org/W201393897","https://openalex.org/W1491144947"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,9,20,24,28,43,53],"limiting":[3,56],"law":[4,57],"of":[5,34,63],"local":[6,54],"field":[7,11,55],"in":[8,19],"mean":[10],"Ghatak-Sherrington":[12],"model":[13],"with":[14],"spin":[15],"values":[16],"$\\{0,\\pm1,\\ldots,\\pm":[17],"S\\}$":[18],"high-temperature":[21],"regime.":[22],"Using":[23],"cavity":[25,45],"method":[26,72],"and":[27,31,73],"quantitative":[29,76],"overlap":[30],"self-overlap":[32],"estimates":[33],"Sheng-Wu~\\cite{SW24},":[35],"we":[36,50],"prove":[37],"a":[38,48,59,75],"central":[39],"limit":[40],"theorem":[41],"for":[42],"non-centered":[44],"field.":[46],"As":[47],"result,":[49],"then":[51],"identify":[52],"as":[58],"random":[60],"finite":[61],"mixture":[62],"Gaussian":[64],"distributions.":[65],"The":[66],"proof":[67],"is":[68],"based":[69],"on":[70],"moment":[71],"gives":[74],"error":[77],"bound.":[78]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-08-14T00:00:00"}