{"id":"https://openalex.org/W7207851285","doi":"https://doi.org/10.48550/arxiv.2609.02682","title":"LDP for Tensor Forms","display_name":"LDP for Tensor Forms","publication_year":2026,"publication_date":"2026-09-02","ids":{"openalex":"https://openalex.org/W7207851285","doi":"https://doi.org/10.48550/arxiv.2609.02682"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.02682","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02682","pdf_url":"https://arxiv.org/pdf/2609.02682","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/2609.02682","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107114022","display_name":"Reihaneh Malekian","orcid":"https://orcid.org/0009-0008-0342-4550","observed_orcids":["https://orcid.org/0009-0008-0342-4550"]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Malekian, Reihaneh","raw_affiliation_strings":["Department of Statistics , Columbia University , New York , NY 10027 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , Columbia University , New York , NY 10027 , USA","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020714633","display_name":"Sohom Bhattacharya","orcid":"https://orcid.org/0000-0001-7445-0096","observed_orcids":["https://orcid.org/0000-0001-7445-0096"]},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bhattacharya, Sohom","raw_affiliation_strings":["Department of Statistics , University of Florida , Gainesville , FL 32603 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of Florida , Gainesville , FL 32603 , USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024944074","display_name":"Nabarun Deb","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Deb, Nabarun","raw_affiliation_strings":["Econometrics and Statistics , University of Chicago Booth School of Business , Chicago , IL 60637 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Econometrics and Statistics , University of Chicago Booth School of Business , Chicago , IL 60637 , USA","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082129067","display_name":"Sumit Mukherjee","orcid":"https://orcid.org/0000-0002-2724-9362","observed_orcids":["https://orcid.org/0000-0002-2724-9362"]},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mukherjee, Sumit","raw_affiliation_strings":["Department of Statistics , Columbia University , New York , NY 10027 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , Columbia University , New York , NY 10027 , USA","institution_ids":["https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.3944999873638153,"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":0.3944999873638153,"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/T11716","display_name":"Random Matrices and Applications","score":0.23280000686645508,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.19580000638961792,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/large-deviations","display_name":"large deviations","score":0.9959999918937683},{"id":"https://openalex.org/keywords/gibbs-measures","display_name":"Gibbs measures","score":0.6430000066757202},{"id":"https://openalex.org/keywords/variational-problems","display_name":"variational problems","score":0.8640000224113464},{"id":"https://openalex.org/keywords/sparse-random-graphs","display_name":"sparse random graphs","score":0.972000002861023},{"id":"https://openalex.org/keywords/potts-model","display_name":"Potts model","score":0.8050000071525574},{"id":"https://openalex.org/keywords/replica-symmetry","display_name":"replica symmetry","score":0.9520000219345093}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7900000214576721},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6927000284194946},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6039999723434448},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5968000292778015},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.534600019454956},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5130000114440918},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.5013999938964844},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.48899999260902405},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4339999854564667},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40959998965263367},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.39719998836517334},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.36230000853538513},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C89128539","wikidata":"https://www.wikidata.org/wiki/Q1949963","display_name":"Statistic","level":2,"score":0.32739999890327454},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.31220000982284546},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.30869999527931213},{"id":"https://openalex.org/C158444337","wikidata":"https://www.wikidata.org/wiki/Q2510435","display_name":"Gibbs measure","level":2,"score":0.3084999918937683},{"id":"https://openalex.org/C88871306","wikidata":"https://www.wikidata.org/wiki/Q7208287","display_name":"Point process","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.2944999933242798},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2897000014781952},{"id":"https://openalex.org/C205301714","wikidata":"https://www.wikidata.org/wiki/Q228249","display_name":"Random measure","level":3,"score":0.28929999470710754},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.27129998803138733},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2628999948501587},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C186515451","wikidata":"https://www.wikidata.org/wiki/Q228191","display_name":"Random sequence","level":3,"score":0.26190000772476196},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.25589999556541443},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.02682","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02682","pdf_url":"https://arxiv.org/pdf/2609.02682","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.2609.02682","doi":"https://doi.org/10.48550/arxiv.2609.02682","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.02682","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:2609.02682","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.02682","pdf_url":"https://arxiv.org/pdf/2609.02682","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":[{"id":"https://openalex.org/G1788317645","display_name":"Mean-Field Models in Statistics","funder_award_id":"2113414","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207851285.pdf","grobid_xml":"https://content.openalex.org/works/W7207851285.grobid-xml"},"referenced_works_count":1,"referenced_works":["https://openalex.org/W7164830168"],"related_works":["https://openalex.org/W4405416028","https://openalex.org/W113348418","https://openalex.org/W2273026252","https://openalex.org/W2050937927","https://openalex.org/W3117122700","https://openalex.org/W4398230283","https://openalex.org/W2079926632","https://openalex.org/W7171572939","https://openalex.org/W4391801131","https://openalex.org/W2921878667"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,35,63,93],"study":[4],"the":[5,19,28,33,46,49,90,100],"large":[6,120],"deviation":[7],"principle":[8],"(LDP)":[9],"for":[10,97,105,118],"a":[11,25,37,41,56,81,119],"tensor-weighted":[12],"functional":[13,57],"of":[14,21,27,48,55,85,99,107,122],"i.i.d.":[15],"random":[16,76],"variables,":[17],"when":[18],"sequence":[20],"tensors":[22],"converges":[23],"under":[24],"variant":[26],"\"bad\"":[29],"cut":[30],"norm.":[31],"Using":[32],"LDP,":[34],"analyze":[36],"Gibbs":[38,124],"measure":[39],"with":[40,126],"tensor-valued":[42],"Hamiltonian,":[43],"and":[44,80],"characterize":[45],"optimizers":[47,109],"limiting":[50],"variational":[51],"problem":[52],"in":[53,74],"terms":[54],"fixed":[58],"point":[59],"equation.":[60],"As":[61],"applications,":[62],"focus":[64],"on":[65],"several":[66],"concrete":[67],"examples,":[68],"which":[69],"include":[70],"monochromatic":[71],"subgraph":[72],"counts":[73],"sparse":[75],"graphs,":[77],"Erd\u0151s-R\u00e9nyi":[78],"hypergraphs,":[79],"generalized":[82],"Potts":[83],"statistic":[84],"order":[86],"$v\\ge":[87],"2$.":[88],"Studying":[89],"optimization":[91],"problem,":[92],"give":[94],"sufficient":[95],"conditions":[96],"uniqueness":[98],"optimizer,":[101],"as":[102,104],"well":[103],"existence":[106],"constant":[108],"(replica":[110],"symmetry).":[111],"Our":[112],"results":[113],"demonstrate":[114],"universal":[115],"weak":[116],"laws":[117],"class":[121],"tensor":[123],"models":[125],"approximately":[127],"regular":[128],"tensors.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-04T00:00:00"}