{"id":"https://openalex.org/W2121413377","doi":"https://doi.org/10.1137/110826333","title":"Selection of Ground States in the Zero Temperature Limit for a One-Parameter Family of Potentials","display_name":"Selection of Ground States in the Zero Temperature Limit for a One-Parameter Family of Potentials","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2121413377","doi":"https://doi.org/10.1137/110826333","mag":"2121413377"},"language":"en","primary_location":{"id":"doi:10.1137/110826333","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110826333","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","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/A5064210321","display_name":"Alexandre Baraviera","orcid":"https://orcid.org/0000-0003-0893-6746"},"institutions":[{"id":"https://openalex.org/I130442723","display_name":"Universidade Federal do Rio Grande do Sul","ror":"https://ror.org/041yk2d64","country_code":"BR","type":"education","lineage":["https://openalex.org/I130442723"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"A. T. Baraviera","raw_affiliation_strings":["Universidade Federal do Rio Grande do Sul"],"affiliations":[{"raw_affiliation_string":"Universidade Federal do Rio Grande do Sul","institution_ids":["https://openalex.org/I130442723"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050207089","display_name":"Renaud Leplaideur","orcid":"https://orcid.org/0000-0003-3960-3901"},"institutions":[{"id":"https://openalex.org/I161929037","display_name":"Universit\u00e9 de Bretagne Occidentale","ror":"https://ror.org/01b8h3982","country_code":"FR","type":"education","lineage":["https://openalex.org/I161929037"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"R. Leplaideur","raw_affiliation_strings":["University of Western Brittany"],"affiliations":[{"raw_affiliation_string":"University of Western Brittany","institution_ids":["https://openalex.org/I161929037"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062442811","display_name":"Artur O. Lopes","orcid":"https://orcid.org/0000-0003-2040-4603"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. O. Lopes","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5064210321"],"corresponding_institution_ids":["https://openalex.org/I130442723"],"apc_list":null,"apc_paid":null,"fwci":2.6679,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.90600579,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"11","issue":"1","first_page":"243","last_page":"260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9995999932289124,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9995999932289124,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9943000078201294,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9904999732971191,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/ergodic-theory","display_name":"Ergodic theory","score":0.7734788060188293},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.7431989312171936},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6494420766830444},{"id":"https://openalex.org/keywords/dirac-measure","display_name":"Dirac measure","score":0.617956280708313},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5762082934379578},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.5527938604354858},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.534630298614502},{"id":"https://openalex.org/keywords/sigma","display_name":"Sigma","score":0.5116267800331116},{"id":"https://openalex.org/keywords/dirac","display_name":"Dirac (video compression format)","score":0.5103787779808044},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.45347219705581665},{"id":"https://openalex.org/keywords/subshift-of-finite-type","display_name":"Subshift of finite type","score":0.4520242214202881},{"id":"https://openalex.org/keywords/ground-state","display_name":"Ground state","score":0.41667285561561584},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38331323862075806},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.38081833720207214},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.3506222367286682},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.3169487416744232},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3014337420463562},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28973519802093506},{"id":"https://openalex.org/keywords/dirac-equation","display_name":"Dirac equation","score":0.2701215147972107},{"id":"https://openalex.org/keywords/dirac-spinor","display_name":"Dirac spinor","score":0.06941458582878113}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.7734788060188293},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7431989312171936},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6494420766830444},{"id":"https://openalex.org/C111118313","wikidata":"https://www.wikidata.org/wiki/Q1227387","display_name":"Dirac measure","level":5,"score":0.617956280708313},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5762082934379578},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.5527938604354858},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.534630298614502},{"id":"https://openalex.org/C2778049214","wikidata":"https://www.wikidata.org/wiki/Q7512234","display_name":"Sigma","level":2,"score":0.5116267800331116},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.5103787779808044},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.45347219705581665},{"id":"https://openalex.org/C105932330","wikidata":"https://www.wikidata.org/wiki/Q7631990","display_name":"Subshift of finite type","level":2,"score":0.4520242214202881},{"id":"https://openalex.org/C69523127","wikidata":"https://www.wikidata.org/wiki/Q4480008","display_name":"Ground state","level":2,"score":0.41667285561561584},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38331323862075806},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.38081833720207214},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.3506222367286682},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.3169487416744232},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3014337420463562},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28973519802093506},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.2701215147972107},{"id":"https://openalex.org/C156785651","wikidata":"https://www.wikidata.org/wiki/Q688945","display_name":"Dirac spinor","level":4,"score":0.06941458582878113},{"id":"https://openalex.org/C149545384","wikidata":"https://www.wikidata.org/wiki/Q5280160","display_name":"Dirac algebra","level":3,"score":0.0},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/110826333","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110826333","pdf_url":null,"source":{"id":"https://openalex.org/S161160597","display_name":"SIAM Journal on Applied Dynamical Systems","issn_l":"1536-0040","issn":["1536-0040"],"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 Applied Dynamical Systems","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03462643v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03462643","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Applied Dynamical Systems, 2012, 11 (1), pp.243-260. &#x27E8;10.1137/110826333&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1488687449","https://openalex.org/W1498335665","https://openalex.org/W1597540527","https://openalex.org/W1969099462","https://openalex.org/W1981313255","https://openalex.org/W2024250320","https://openalex.org/W2036776909","https://openalex.org/W2056945854","https://openalex.org/W2068983872","https://openalex.org/W2102623353","https://openalex.org/W2128746881","https://openalex.org/W2129934442","https://openalex.org/W2153166277","https://openalex.org/W2162279258","https://openalex.org/W2321686938","https://openalex.org/W2329051460","https://openalex.org/W2600289236","https://openalex.org/W2963582215","https://openalex.org/W2963812652","https://openalex.org/W3099764977","https://openalex.org/W3104076591","https://openalex.org/W4255454912"],"related_works":["https://openalex.org/W3042893665","https://openalex.org/W4287713897","https://openalex.org/W2027267123","https://openalex.org/W2360630817","https://openalex.org/W2092696287","https://openalex.org/W2300735334","https://openalex.org/W1972218875","https://openalex.org/W2148912761","https://openalex.org/W890486392","https://openalex.org/W2808318012"],"abstract_inverted_index":{"For":[0],"the":[1,9,12,18,46,68,72,75,78,90,115,120,125,128,135,139,142,149,152,155,158,161,165,168,171],"subshift":[2],"of":[3,17,52,89,127,138],"finite":[4,116],"type":[5],"$\\Sigma=\\{0,1,2\\}^{\\mathbb{N}}$":[6],"we":[7,133],"study":[8],"convergence":[10,63],"and":[11,45,157],"selection":[13],"at":[14,40,50,71],"temperature":[15],"zero":[16],"Gibbs":[19,140],"measure":[20,70,147],"associated":[21],"to":[22,67,83,114,124],"a":[23],"non\u2013locally":[24],"constant":[25],"H\u00f6lder":[26],"potential":[27,47,76,153,169],"which":[28],"admits":[29],"exactly":[30],"two":[31,41,54,129],"maximizing":[32],"ergodic":[33],"measures.":[34,131],"These":[35],"measures":[36,39],"are":[37],"Dirac":[38,69,130,146],"different":[42],"fixed":[43,55],"points,":[44],"is":[48,62,77,81,111,154,170],"flatter":[49],"one":[51,145,163],"these":[53],"points.":[56],"We":[57],"prove":[58],"that":[59],"there":[60],"always":[61],"but":[64],"not":[65],"necessarily":[66],"point":[73,150,166],"where":[74,119,151,167],"flattest.":[79],"This":[80,110],"contrary":[82,113],"what":[84],"was":[85],"expected":[86],"in":[87,93],"light":[88],"analogous":[91],"problem":[92],"Aubry-Mather":[94],"theory":[95],"[N.":[96],"Anantharaman":[97],"et":[98],"al.,":[99],"Discrete":[100],"Contin.":[101],"Dyn.":[102],"Syst.":[103],"Ser.":[104],"B,":[105],"5":[106],"(2005),":[107],"pp.":[108],"513\u2013528].":[109],"also":[112],"range":[117],"case":[118],"equilibrium":[121],"state":[122],"converges":[123],"equi-barycenter":[126],"Moreover,":[132],"emphasize":[134],"unexpected":[136],"behavior":[137],"measure:":[141],"eigenmeasure":[143],"selects":[144,160],"(at":[148,164],"flattest),":[156],"eigenfunction":[159],"other":[162],"sharpest).":[172]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
