{"id":"https://openalex.org/W4388226807","doi":"https://doi.org/10.1137/22m1519717","title":"A Selection Principle for Weak KAM Solutions via Freidlin\u2013Wentzell Large Deviation Principle of Invariant Measures","display_name":"A Selection Principle for Weak KAM Solutions via Freidlin\u2013Wentzell Large Deviation Principle of Invariant Measures","publication_year":2023,"publication_date":"2023-11-02","ids":{"openalex":"https://openalex.org/W4388226807","doi":"https://doi.org/10.1137/22m1519717"},"language":"en","primary_location":{"id":"doi:10.1137/22m1519717","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1519717","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006821457","display_name":"Yuan Gao","orcid":"https://orcid.org/0000-0002-7231-5672"},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yuan Gao","raw_affiliation_strings":["Department of Mathematics, Purdue University, West Lafayette, IN 47907 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Purdue University, West Lafayette, IN 47907 USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019169169","display_name":"Jian\u2010Guo Liu","orcid":"https://orcid.org/0000-0002-9911-4045"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jian-Guo Liu","raw_affiliation_strings":["Department of Mathematics and Department of Physics, Duke University, Durham, NC 22708 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Department of Physics, Duke University, Durham, NC 22708 USA","institution_ids":["https://openalex.org/I170897317"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006821457"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":null,"apc_paid":null,"fwci":1.1447,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.76864105,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"55","issue":"6","first_page":"6457","last_page":"6495"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8366876840591431},{"id":"https://openalex.org/keywords/rate-function","display_name":"Rate function","score":0.7877638339996338},{"id":"https://openalex.org/keywords/large-deviations-theory","display_name":"Large deviations theory","score":0.6151027679443359},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6036701202392578},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5832047462463379},{"id":"https://openalex.org/keywords/variational-principle","display_name":"Variational principle","score":0.537276566028595},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.5203463435173035},{"id":"https://openalex.org/keywords/kolmogorov\u2013arnold\u2013moser-theorem","display_name":"Kolmogorov\u2013Arnold\u2013Moser theorem","score":0.5054552555084229},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.455667644739151},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.42454013228416443},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.25572556257247925},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.2261069118976593}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8366876840591431},{"id":"https://openalex.org/C15964574","wikidata":"https://www.wikidata.org/wiki/Q7295534","display_name":"Rate function","level":3,"score":0.7877638339996338},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.6151027679443359},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6036701202392578},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5832047462463379},{"id":"https://openalex.org/C9259290","wikidata":"https://www.wikidata.org/wiki/Q745215","display_name":"Variational principle","level":2,"score":0.537276566028595},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.5203463435173035},{"id":"https://openalex.org/C8522634","wikidata":"https://www.wikidata.org/wiki/Q587081","display_name":"Kolmogorov\u2013Arnold\u2013Moser theorem","level":3,"score":0.5054552555084229},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.455667644739151},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.42454013228416443},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.25572556257247925},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2261069118976593},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1519717","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1519717","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.8899999856948853,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G5046989123","display_name":null,"funder_award_id":"DMS-2204288","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6871508810","display_name":null,"funder_award_id":"DMS-2106988","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W114441229","https://openalex.org/W897674100","https://openalex.org/W1487586009","https://openalex.org/W1706053453","https://openalex.org/W1967120384","https://openalex.org/W1970111697","https://openalex.org/W1982142979","https://openalex.org/W1982843064","https://openalex.org/W1990390116","https://openalex.org/W1997714823","https://openalex.org/W1999897837","https://openalex.org/W2014608293","https://openalex.org/W2027438381","https://openalex.org/W2029188814","https://openalex.org/W2036776909","https://openalex.org/W2036807120","https://openalex.org/W2050098476","https://openalex.org/W2052408997","https://openalex.org/W2053068479","https://openalex.org/W2068950196","https://openalex.org/W2074685809","https://openalex.org/W2076319278","https://openalex.org/W2093711514","https://openalex.org/W2128746881","https://openalex.org/W2130246597","https://openalex.org/W2138710479","https://openalex.org/W2139325298","https://openalex.org/W2289075724","https://openalex.org/W2749408143","https://openalex.org/W2963552545","https://openalex.org/W2964141422","https://openalex.org/W2985032492","https://openalex.org/W3003570566","https://openalex.org/W3102502737","https://openalex.org/W3103048269","https://openalex.org/W3103862770","https://openalex.org/W3203531525","https://openalex.org/W4242843002","https://openalex.org/W4249520102","https://openalex.org/W4294636440","https://openalex.org/W4318038002"],"related_works":["https://openalex.org/W1983345526","https://openalex.org/W2076944689","https://openalex.org/W2061585064","https://openalex.org/W1594944678","https://openalex.org/W1977330547","https://openalex.org/W1487586009","https://openalex.org/W3102569876","https://openalex.org/W2971079383","https://openalex.org/W1997500459","https://openalex.org/W2061850819"],"abstract_inverted_index":{".This":[0],"paper":[1],"reinterprets":[2],"the":[3,8,12,20,39,45,49,58,63,70,74,78,82,90,97,104,109,113,144,149,164,171],"Freidlin\u2013Wentzell":[4,59,105],"variational":[5,60,106],"construction":[6,61,180],"of":[7,57,62,148,181],"rate":[9,64,87],"function":[10,65,88],"in":[11,38],"large":[13],"deviation":[14],"principle":[15],"for":[16,73,108,155],"invariant":[17],"measures":[18],"from":[19,81],"weak":[21,40,54,131,192],"KAM":[22,41,55,132,193],"perspective.":[23],"Through":[24],"a":[25,31,129,178],"one-dimensional":[26],"irreversible":[27],"diffusion":[28],"process":[29],"on":[30,69,112],"torus,":[32],"we":[33],"explicitly":[34],"characterize":[35],"essential":[36,126],"concepts":[37],"theory,":[42],"such":[43],"as":[44,143],"Peierls":[46,84],"barrier":[47],"and":[48,77,168],"projected":[50],"Mather/Aubry/Ma\u00f1\u00e9":[51],"sets.":[52],"The":[53],"representation":[56],"is":[66,125],"discussed":[67],"based":[68],"global":[71,145],"adjustment":[72],"boundary":[75,110,119],"data":[76,111,120],"local":[79,123],"trimming":[80],"lifted":[83],"barriers.":[85],"This":[86,137,153],"gives":[89],"maximal":[91],"Lipschitz":[92,186],"continuous":[93,187],"viscosity":[94,139,183,188],"solution":[95,133,140],"to":[96,127,134],"corresponding":[98],"stationary":[99,135,156],"Hamilton\u2013Jacobi":[100],"equation":[101],"(HJE),":[102],"satisfying":[103],"formula":[107],"Aubry":[114],"set.":[115],"Choosing":[116],"meaningful":[117],"self-consistent":[118],"at":[121],"each":[122],"attractor":[124],"select":[128],"unique":[130],"HJE.":[136],"selected":[138],"also":[141,176],"serves":[142],"energy":[146,190],"landscape":[147],"original":[150],"stochastic":[151],"process.":[152],"selection":[154],"HJEs":[157],"can":[158],"be":[159],"described":[160],"by":[161],"first":[162],"taking":[163,170],"long":[165],"time":[166],"limit":[167],"then":[169],"zero":[172],"noise":[173],"limit,":[174],"which":[175],"provides":[177],"special":[179],"vanishing":[182],"approximation.KeywordsAubry\u2013Mather":[184],"theorymaximal":[185],"solutionglobal":[189],"landscapediscrete":[191],"problemirreversible":[194],"processLax\u2013Oleinik":[195],"semigroupMSC":[196],"codes37J5060F1049L25":[197]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}