{"id":"https://openalex.org/W4407150873","doi":"https://doi.org/10.4171/mems/16","title":"Stochastic Quantization of the \ud835\udedf\u00b3\u2083-Model","display_name":"Stochastic Quantization of the \ud835\udedf\u00b3\u2083-Model","publication_year":2025,"publication_date":"2025-02-05","ids":{"openalex":"https://openalex.org/W4407150873","doi":"https://doi.org/10.4171/mems/16","mag":"3195437615"},"language":"en","primary_location":{"id":"doi:10.4171/mems/16","doi":"https://doi.org/10.4171/mems/16","is_oa":true,"landing_page_url":"https://doi.org/10.4171/mems/16","pdf_url":"https://ems.press/content/book-files/49924","source":{"id":"https://openalex.org/S4393919431","display_name":"Memoirs of the European Mathematical Society","issn_l":"2747-9080","issn":["2747-9080","2747-9099"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Memoirs of the European Mathematical Society","raw_type":"monograph"},"volume":null,"type":"book","is_traditional":true,"indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://ems.press/content/book-files/49924","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090720658","display_name":"Tadahiro Oh","orcid":"https://orcid.org/0000-0003-2313-1145","observed_orcids":["https://orcid.org/0000-0003-2313-1145"]},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]},{"id":"https://openalex.org/I4210117017","display_name":"Maxwell Institute for Mathematical Sciences","ror":"https://ror.org/02tsqtg57","country_code":"GB","type":"facility","lineage":["https://openalex.org/I32062511","https://openalex.org/I4210117017","https://openalex.org/I98677209"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["CN","GB"],"is_corresponding":false,"raw_author_name":"Tadahiro Oh","raw_affiliation_strings":["Beijing Institute of Technology","Maxwell Institute for Mathematical Sciences, Edinburgh, UK","University of Edinburgh"],"raw_orcid":"https://orcid.org/0000-0003-2313-1145","affiliations":[{"raw_affiliation_string":"Beijing Institute of Technology","institution_ids":["https://openalex.org/I125839683"]},{"raw_affiliation_string":"Maxwell Institute for Mathematical Sciences, Edinburgh, UK","institution_ids":["https://openalex.org/I4210117017"]},{"raw_affiliation_string":"University of Edinburgh","institution_ids":["https://openalex.org/I98677209"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069067766","display_name":"Mamoru Okamoto","orcid":"https://orcid.org/0000-0003-2667-4268","observed_orcids":["https://orcid.org/0000-0003-2667-4268"]},"institutions":[{"id":"https://openalex.org/I98285908","display_name":"The University of Osaka","ror":"https://ror.org/035t8zc32","country_code":"JP","type":"education","lineage":["https://openalex.org/I98285908"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Mamoru Okamoto","raw_affiliation_strings":["Osaka University, Japan"],"raw_orcid":"https://orcid.org/0000-0003-2667-4268","affiliations":[{"raw_affiliation_string":"Osaka University, Japan","institution_ids":["https://openalex.org/I98285908"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073623168","display_name":"Leonardo Tolomeo","orcid":"https://orcid.org/0000-0002-1882-2294","observed_orcids":["https://orcid.org/0000-0002-1882-2294"]},"institutions":[{"id":"https://openalex.org/I135140700","display_name":"University of Bonn","ror":"https://ror.org/041nas322","country_code":"DE","type":"education","lineage":["https://openalex.org/I135140700"]},{"id":"https://openalex.org/I4210117017","display_name":"Maxwell Institute for Mathematical Sciences","ror":"https://ror.org/02tsqtg57","country_code":"GB","type":"facility","lineage":["https://openalex.org/I32062511","https://openalex.org/I4210117017","https://openalex.org/I98677209"]},{"id":"https://openalex.org/I98677209","display_name":"University of Edinburgh","ror":"https://ror.org/01nrxwf90","country_code":"GB","type":"education","lineage":["https://openalex.org/I98677209"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Leonardo Tolomeo","raw_affiliation_strings":["Maxwell Institute for Mathematical Sciences, Edinburgh, UK","University of Bonn","University of Edinburgh"],"raw_orcid":"https://orcid.org/0000-0002-1882-2294","affiliations":[{"raw_affiliation_string":"Maxwell Institute for Mathematical Sciences, Edinburgh, UK","institution_ids":["https://openalex.org/I4210117017"]},{"raw_affiliation_string":"University of Bonn","institution_ids":["https://openalex.org/I135140700"]},{"raw_affiliation_string":"University of Edinburgh","institution_ids":["https://openalex.org/I98677209"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":10.0386,"has_fulltext":true,"cited_by_count":38,"citation_normalized_percentile":{"value":0.97979798,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.5303000211715698,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.5303000211715698,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.2581000030040741,"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.08749999850988388,"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/gibbs-measures","display_name":"Gibbs measures","score":0.628000020980835},{"id":"https://openalex.org/keywords/stochastic-quantization","display_name":"stochastic quantization","score":0.8159999847412109},{"id":"https://openalex.org/keywords/optimal-transport","display_name":"optimal transport","score":0.9760000109672546},{"id":"https://openalex.org/keywords/global-well-posedness","display_name":"global well-posedness","score":0.9390000104904175},{"id":"https://openalex.org/keywords/additive-space-time-white-noise","display_name":"additive space-time white noise","score":0.7369999885559082},{"id":"https://openalex.org/keywords/phase-transitions","display_name":"phase transitions","score":0.4749999940395355}],"concepts":[{"id":"https://openalex.org/C2780288589","wikidata":"https://www.wikidata.org/wiki/Q7617833","display_name":"Stochastic quantization","level":4,"score":0.7333710789680481},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.48686710000038147},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45521870255470276},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32433822751045227},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17196983098983765},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12936529517173767},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.07474425435066223},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154018700","wikidata":"https://www.wikidata.org/wiki/Q898323","display_name":"Path integral formulation","level":3,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.4171/mems/16","doi":"https://doi.org/10.4171/mems/16","is_oa":true,"landing_page_url":"https://doi.org/10.4171/mems/16","pdf_url":"https://ems.press/content/book-files/49924","source":{"id":"https://openalex.org/S4393919431","display_name":"Memoirs of the European Mathematical Society","issn_l":"2747-9080","issn":["2747-9080","2747-9099"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Memoirs of the European Mathematical Society","raw_type":"monograph"},{"id":"pmh:oai:arXiv.org:2108.06777","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2108.06777","pdf_url":"https://arxiv.org/pdf/2108.06777","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":"mag:3195437615","doi":null,"is_oa":true,"landing_page_url":"http://export.arxiv.org/pdf/2108.06777","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:pure.ed.ac.uk:openaire/30bdde38-6294-4516-a0ac-0d476159da39","doi":null,"is_oa":true,"landing_page_url":"https://www.research.ed.ac.uk/files/493329740/Phi33_final.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400321","display_name":"Edinburgh Research Explorer (University of Edinburgh)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I98677209","host_organization_name":"University of Edinburgh","host_organization_lineage":["https://openalex.org/I98677209"],"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":"Oh, T, Okamoto, M & Tolomeo, L 2025, Stochastic quantization of the \u03a6^3_3-model. Memoirs of the European Mathematical Society, vol. 16, EMS Press. https://doi.org/10.4171/MEMS/16","raw_type":"info:eu-repo/semantics/book"},{"id":"doi:10.48550/arxiv.2108.06777","doi":"https://doi.org/10.48550/arxiv.2108.06777","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2108.06777","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":"doi:10.4171/mems/16","doi":"https://doi.org/10.4171/mems/16","is_oa":true,"landing_page_url":"https://doi.org/10.4171/mems/16","pdf_url":"https://ems.press/content/book-files/49924","source":{"id":"https://openalex.org/S4393919431","display_name":"Memoirs of the European Mathematical Society","issn_l":"2747-9080","issn":["2747-9080","2747-9099"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Memoirs of the European Mathematical Society","raw_type":"monograph"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G11009315","display_name":null,"funder_award_id":"CRC 1060","funder_id":"https://openalex.org/F4320328568","funder_display_name":"Hausdorff Center for Mathematics"},{"id":"https://openalex.org/G1521016025","display_name":"EXC 2047: Hausdorff Center for Mathematics (HCM)","funder_award_id":"390685813","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G1600773818","display_name":null,"funder_award_id":"EXC 2047/1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G2669770870","display_name":"\u6975\u4f53\u5f62\u6210\u6a5f\u69cb\u306e\u7814\u7a76","funder_award_id":"864138","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G3655418302","display_name":null,"funder_award_id":"CRC 1060","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4130143441","display_name":"Study on asymptotic behavior and singularities of solutions for nonlinear dispersive equations by using geometric symmetry","funder_award_id":"20K14342","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G4274133347","display_name":null,"funder_award_id":"390685813","funder_id":"https://openalex.org/F4320328568","funder_display_name":"Hausdorff Center for Mathematics"},{"id":"https://openalex.org/G4879533116","display_name":null,"funder_award_id":"211504053","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G591746060","display_name":null,"funder_award_id":"EXC-2047","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8118356716","display_name":"SFB 1060: Die Mathematik der emergenten Effekte","funder_award_id":"211504053","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8372877233","display_name":null,"funder_award_id":"211504053","funder_id":"https://openalex.org/F4320328568","funder_display_name":"Hausdorff Center for Mathematics"},{"id":"https://openalex.org/G951816307","display_name":null,"funder_award_id":"637995","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320328568","display_name":"Hausdorff Center for Mathematics","ror":"https://ror.org/032n1tr36"},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407150873.pdf","grobid_xml":"https://content.openalex.org/works/W4407150873.grobid-xml"},"referenced_works_count":53,"referenced_works":["https://openalex.org/W166242285","https://openalex.org/W1489373617","https://openalex.org/W1530034100","https://openalex.org/W1542004730","https://openalex.org/W1554577510","https://openalex.org/W1573631469","https://openalex.org/W1585160083","https://openalex.org/W1587955208","https://openalex.org/W1705585130","https://openalex.org/W1964699420","https://openalex.org/W1965612019","https://openalex.org/W1990089063","https://openalex.org/W2002465072","https://openalex.org/W2008622900","https://openalex.org/W2014336342","https://openalex.org/W2028212348","https://openalex.org/W2036457739","https://openalex.org/W2093649432","https://openalex.org/W2094531750","https://openalex.org/W2095025992","https://openalex.org/W2102327241","https://openalex.org/W2109291478","https://openalex.org/W2117259115","https://openalex.org/W2125433609","https://openalex.org/W2125624906","https://openalex.org/W2152132117","https://openalex.org/W2152743516","https://openalex.org/W2160143589","https://openalex.org/W2180740707","https://openalex.org/W2226817846","https://openalex.org/W2283292583","https://openalex.org/W2319542184","https://openalex.org/W2327509254","https://openalex.org/W2602868920","https://openalex.org/W2608191236","https://openalex.org/W2735221084","https://openalex.org/W2765651384","https://openalex.org/W2770599597","https://openalex.org/W2799083984","https://openalex.org/W2932006791","https://openalex.org/W2963627731","https://openalex.org/W2963849077","https://openalex.org/W3005483704","https://openalex.org/W3032696030","https://openalex.org/W3084031666","https://openalex.org/W3097988259","https://openalex.org/W3119761404","https://openalex.org/W3123828668","https://openalex.org/W3148772014","https://openalex.org/W3189840808","https://openalex.org/W3200345558","https://openalex.org/W4387356351","https://openalex.org/W7140185509"],"related_works":["https://openalex.org/W4287024742","https://openalex.org/W3195437615","https://openalex.org/W7051947027","https://openalex.org/W2972884704","https://openalex.org/W3084031666","https://openalex.org/W4396222306","https://openalex.org/W2770599597","https://openalex.org/W4323657450","https://openalex.org/W4415198304","https://openalex.org/W2885847720"],"abstract_inverted_index":{"We":[0],"study":[1,183],"the":[2,5,11,14,17,38,42,50,63,80,87,94,98,104,109,112,119,149,164,184,188,193,198,217,223,229,235,246,258,266,270,274,291,296],"construction":[3],"of":[4,16,49,103,111,148,192,257,265,304],"\u02c63":[6,51,81,105,113,150,166,194,219,260],"3":[7,52,82,106,114,151,167,195,220,261],"-measure":[8,53,83,115,152],"and":[9,25,54,153,234,244,263,283,300],"complete":[10],"program":[12],"on":[13],"(non-)construction":[15],"focusing":[18],"Gibbs":[19,267,293],"measures,":[20],"initiated":[21],"by":[22,91,97,210,231,245],"Lebowitz,":[23],"Rose,":[24],"Speer":[26],"[J.Statist.Phys.50":[27],"(1988),":[28],"no.3-4,":[29],"657-687].This":[30],"problem":[31,186],"turns":[32],"out":[33],"to":[34,62,78,108,118,133,138,179],"be":[35],"critical,":[36],"exhibiting":[37],"following":[39],"phase":[40],"transition.In":[41],"weakly":[43,271],"nonlinear":[44,89,202,272],"regime,":[45,90],"we":[46,68,100,142,161,251,277,287],"prove":[47,162,252],"normalizability":[48],"show":[55,69,154],"that":[56,70,155,163],"it":[57],"is":[58,84,158],"singular":[59],"with":[60,76,116,205,290],"respect":[61,77,117],"massive":[64,120],"Gaussian":[65,121],"free":[66,122],"field.Moreover,":[67],"there":[71],"exists":[72],"a":[73,128,145,174,180,206,279],"shifted":[74],"measure":[75,157,268],"which":[79],"absolutely":[85],"continuous.In":[86],"strongly":[88],"further":[92],"developing":[93],"machinery":[95],"introduced":[96],"authors,":[99],"establish":[101],"non-normalizability":[102,125],"-measure.Due":[107],"singularity":[110],"field,":[123],"this":[124,140,156],"part":[126],"poses":[127],"particular":[129,227],"challenge":[130],"as":[131],"compared":[132],"our":[134],"previous":[135],"works.In":[136],"order":[137],"overcome":[139],"issue,":[141],"first":[143,236],"construct":[144],"-finite":[146],"version":[147],"not":[159],"normalizable.Furthermore,":[160],"truncated":[165],"-measures":[168],"have":[169],"no":[170],"weak":[171],"limit":[172],"in":[173,226,269],"natural":[175],"space,":[176],"even":[177],"up":[178],"subsequence.We":[181],"also":[182],"dynamical":[185],"for":[187],"canonical":[189],"stochastic":[190,200],"quantization":[191],"-measure,":[196],"namely,":[197],"three-dimensional":[199],"damped":[201],"wave":[203],"equation":[204],"quadratic":[207],"nonlinearity":[208],"forced":[209],"an":[211],"additive":[212],"space-time":[213],"white":[214],"noise":[215],"(=":[216],"hyperbolic":[218,259],"-model).By":[221],"adapting":[222],"paracontrolled":[224],"approach,":[225,285],"from":[228,302],"works":[230],"Gubinelli,":[232],"Koch,":[233],"author":[237],"[J.Eur.Math.Soc.":[238],"26":[239],"(2024),":[240,249],"no.":[241],"3,":[242],"817-874]":[243],"authors":[247],"[Mem.Amer.Math.Soc.304":[248],"no.1529],":[250],"almost":[253],"sure":[254],"global":[255],"well-posedness":[256],"-model":[262],"invariance":[264],"regime.In":[273],"globalization":[275],"part,":[276],"introduce":[278],"new,":[280],"conceptually":[281],"simple":[282],"straightforward":[284],"where":[286],"directly":[288],"work":[289],"(truncated)":[292],"measure,":[294],"using":[295],"Bou\u00e9-Dupuis":[297],"variational":[298],"formula":[299],"ideas":[301],"theory":[303],"optimal":[305],"transport.":[306]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2025-02-05T00:00:00"}
