{"id":"https://openalex.org/W2961264525","doi":"https://doi.org/10.1137/19m1296859","title":"Coulomb Gases Under Constraint: Some Theoretical and Numerical Results","display_name":"Coulomb Gases Under Constraint: Some Theoretical and Numerical Results","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2961264525","doi":"https://doi.org/10.1137/19m1296859","mag":"2961264525"},"language":"en","primary_location":{"id":"doi:10.1137/19m1296859","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1296859","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1907.05803","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015541993","display_name":"Djalil Chafa\u00ef","orcid":"https://orcid.org/0000-0002-1446-1428"},"institutions":[{"id":"https://openalex.org/I171048554","display_name":"Centre de Recherche en Math\u00e9matiques de la D\u00e9cision","ror":"https://ror.org/03s0gj002","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I171048554","https://openalex.org/I2746051580","https://openalex.org/I4210141950","https://openalex.org/I56435720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Djalil Chafa\u00ef","raw_affiliation_strings":["CEREMADE - CEntre de REcherches en MAth\u00e9matiques de la DEcision (Place du Mar\u00e9chal de Lattre de Tassigny 75775 - Paris Cedex 16 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CEREMADE - CEntre de REcherches en MAth\u00e9matiques de la DEcision (Place du Mar\u00e9chal de Lattre de Tassigny 75775 - Paris Cedex 16 - France)","institution_ids":["https://openalex.org/I171048554"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055239160","display_name":"Gr\u00e9goire Ferr\u00e9","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gr\u00e9goire Ferr\u00e9","raw_affiliation_strings":["MATHERIALS - MATHematics for MatERIALS (France)","CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MATHERIALS - MATHematics for MatERIALS (France)","institution_ids":[]},{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015347592","display_name":"Gabriel Stoltz","orcid":"https://orcid.org/0000-0002-2797-5938"},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gabriel Stoltz","raw_affiliation_strings":["CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","MATHERIALS - MATHematics for MatERIALS (France)"],"raw_orcid":"https://orcid.org/0000-0002-2797-5938","affiliations":[{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]},{"raw_affiliation_string":"MATHERIALS - MATHematics for MatERIALS (France)","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9343,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75461869,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"53","issue":"1","first_page":"181","last_page":"220"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9994999766349792,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9994999766349792,"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/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9972000122070312,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.996399998664856,"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/measure","display_name":"Measure (data warehouse)","score":0.6439485549926758},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5775554180145264},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5702766180038452},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4978830814361572},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4937492311000824},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4748131036758423},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4735790193080902},{"id":"https://openalex.org/keywords/coulomb","display_name":"Coulomb","score":0.4374789595603943},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4277762770652771},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.40503960847854614},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.28740090131759644},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2522166967391968},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12565824389457703},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11650452017784119}],"concepts":[{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.6439485549926758},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5775554180145264},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5702766180038452},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4978830814361572},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4937492311000824},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4748131036758423},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4735790193080902},{"id":"https://openalex.org/C9342510","wikidata":"https://www.wikidata.org/wiki/Q25406","display_name":"Coulomb","level":3,"score":0.4374789595603943},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4277762770652771},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40503960847854614},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.28740090131759644},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2522166967391968},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12565824389457703},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11650452017784119},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C147120987","wikidata":"https://www.wikidata.org/wiki/Q2225","display_name":"Electron","level":2,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/19m1296859","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1296859","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"},{"id":"pmh:oai:arXiv.org:1907.05803","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.05803","pdf_url":"https://arxiv.org/pdf/1907.05803","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:HAL:hal-02184896v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02184896","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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 Mathematical Analysis, 2021, 53 (1), pp.181-220. ⟨10.1137/19M1296859⟩","raw_type":"Journal articles"},{"id":"pmh:oai:basepub.dauphine.fr:123456789/20181","is_oa":false,"landing_page_url":"https://basepub.dauphine.fr/handle/123456789/20181","pdf_url":null,"source":{"id":"https://openalex.org/S4306401007","display_name":"Base Institutionnelle de Recherche de l'universit\u00e9 Paris-Dauphine (BIRD) (University Paris-Dauphine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102197404","host_organization_name":"Universit\u00e9 Paris-Sud","host_organization_lineage":["https://openalex.org/I102197404"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Document de travail / Working paper"},{"id":"pmh:oai:basepub.dauphine.psl.eu:123456789/20181","is_oa":false,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-02184896","pdf_url":null,"source":{"id":"https://openalex.org/S4306401007","display_name":"Base Institutionnelle de Recherche de l'universit\u00e9 Paris-Dauphine (BIRD) (University Paris-Dauphine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102197404","host_organization_name":"Universit\u00e9 Paris-Sud","host_organization_lineage":["https://openalex.org/I102197404"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Document de travail / Working paper"},{"id":"pmh:oai:basepub.dauphine.psl.eu:123456789/22349","is_oa":true,"landing_page_url":"https://basepub.dauphine.psl.eu/handle/123456789/22349","pdf_url":null,"source":{"id":"https://openalex.org/S4306401007","display_name":"Base Institutionnelle de Recherche de l'universit\u00e9 Paris-Dauphine (BIRD) (University Paris-Dauphine)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102197404","host_organization_name":"Universit\u00e9 Paris-Sud","host_organization_lineage":["https://openalex.org/I102197404"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article accept\u00e9 pour publication ou publi\u00e9"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1907.05803","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.05803","pdf_url":"https://arxiv.org/pdf/1907.05803","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.6899999976158142}],"awards":[{"id":"https://openalex.org/G1827871001","display_name":null,"funder_award_id":"ANR-10-LABX-58-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3100797910","display_name":"Entropy, flows, inequalities","funder_award_id":"ANR-17-CE40-0030","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3336046209","display_name":"COmputational Statistics and MOlecular Simulation","funder_award_id":"ANR-14-CE23-0012","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G7236940437","display_name":null,"funder_award_id":"614492","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":63,"referenced_works":["https://openalex.org/W887980625","https://openalex.org/W1489238841","https://openalex.org/W1544770838","https://openalex.org/W1573264833","https://openalex.org/W1575130722","https://openalex.org/W1585160083","https://openalex.org/W1738603105","https://openalex.org/W1793259860","https://openalex.org/W1812558952","https://openalex.org/W1970723308","https://openalex.org/W2001381073","https://openalex.org/W2001504669","https://openalex.org/W2036073493","https://openalex.org/W2052831210","https://openalex.org/W2065955445","https://openalex.org/W2071175738","https://openalex.org/W2073488922","https://openalex.org/W2078645667","https://openalex.org/W2081302937","https://openalex.org/W2091004357","https://openalex.org/W2129351457","https://openalex.org/W2139812092","https://openalex.org/W2163037972","https://openalex.org/W2163974134","https://openalex.org/W2203710570","https://openalex.org/W2527794494","https://openalex.org/W2545581449","https://openalex.org/W2592528128","https://openalex.org/W2768264776","https://openalex.org/W2772905648","https://openalex.org/W2787796577","https://openalex.org/W2798525442","https://openalex.org/W2799499928","https://openalex.org/W2807970565","https://openalex.org/W2820111529","https://openalex.org/W2901706448","https://openalex.org/W2913426266","https://openalex.org/W2961264525","https://openalex.org/W2962773076","https://openalex.org/W2962846798","https://openalex.org/W2962905242","https://openalex.org/W2963419102","https://openalex.org/W2964232626","https://openalex.org/W2973029036","https://openalex.org/W2975299872","https://openalex.org/W2994633184","https://openalex.org/W3016344659","https://openalex.org/W3020454757","https://openalex.org/W3098028924","https://openalex.org/W3100118712","https://openalex.org/W3102493690","https://openalex.org/W3102719200","https://openalex.org/W3103791480","https://openalex.org/W3105109562","https://openalex.org/W3105339266","https://openalex.org/W3105527479","https://openalex.org/W3158609243","https://openalex.org/W4210869902","https://openalex.org/W4256467805","https://openalex.org/W4287990834","https://openalex.org/W4299643759","https://openalex.org/W4300957459","https://openalex.org/W4380199382"],"related_works":["https://openalex.org/W4255837520","https://openalex.org/W2387011115","https://openalex.org/W4234808182","https://openalex.org/W2382043075","https://openalex.org/W2809151339","https://openalex.org/W2216913934","https://openalex.org/W2393870460","https://openalex.org/W3156661037","https://openalex.org/W2360673138","https://openalex.org/W2809370583"],"abstract_inverted_index":{"We":[0,27,40],"consider":[1],"Coulomb":[2],"gas":[3,33],"models":[4],"for":[5,172,178],"which":[6,156],"the":[7,13,29,32,44,63,67,72,97,108,116,122,127,175],"empirical":[8],"measure":[9,22,125],"typically":[10],"concentrates,":[11],"when":[12,31],"number":[14],"of":[15,47,70,74,115,129],"particles":[16,75],"becomes":[17],"large,":[18],"on":[19,36,90,138,142],"an":[20,24,112],"equilibrium":[21,124],"minimizing":[23],"electrostatic":[25],"energy.":[26,117],"study":[28],"behavior":[30],"is":[34,53,111,160],"conditioned":[35,123,176],"a":[37,58,85,91,130,166,179],"rare":[38],"event.":[39],"first":[41],"show":[42],"that":[43,62,107],"special":[45],"case":[46],"quadratic":[48,143],"confinement":[49],"and":[50,61,141,152],"linear":[51,139],"constraint":[52],"exactly":[54],"solvable":[55],"due":[56],"to":[57,105,120],"remarkable":[59],"factorization,":[60],"conditioning":[64,99,109],"has":[65],"then":[66],"simple":[68],"effect":[69],"shifting":[71],"cloud":[73],"without":[76],"deformation.":[77],"To":[78],"address":[79],"more":[80],"general":[81],"cases,":[82],"we":[83,136,147,164],"perform":[84],"theoretical":[86],"asymptotic":[87],"analysis":[88],"relying":[89],"large":[92,182],"deviations":[93],"technique":[94],"known":[95],"as":[96,126],"Gibbs":[98],"principle.":[100],"The":[101],"technical":[102],"part":[103],"amounts":[104],"establishing":[106],"ensemble":[110],"$I$-continuity":[113],"set":[114],"This":[118],"leads":[119],"characterizing":[121],"solution":[128,159],"modified":[131],"variational":[132],"problem.":[133],"For":[134,162],"simplicity,":[135],"focus":[137],"statistics":[140,144],"constraints.":[145],"Finally,":[146],"numerically":[148],"illustrate":[149],"our":[150],"predictions":[151],"explore":[153],"cases":[154],"in":[155],"no":[157],"explicit":[158],"known.":[161],"this,":[163],"use":[165],"generalized":[167],"hybrid":[168],"Monte":[169],"Carlo":[170],"algorithm":[171],"sampling":[173],"from":[174],"distribution":[177],"finite":[180],"but":[181],"system.":[183]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-22T08:00:12.763002","created_date":"2025-10-10T00:00:00"}