{"id":"https://openalex.org/W4415159419","doi":"https://doi.org/10.1137/25m1751347","title":"Wasserstein Convergence Rates for Stochastic Particle Approximation of Boltzmann Models","display_name":"Wasserstein Convergence Rates for Stochastic Particle Approximation of Boltzmann Models","publication_year":2026,"publication_date":"2026-04-10","ids":{"openalex":"https://openalex.org/W4415159419","doi":"https://doi.org/10.1137/25m1751347"},"language":"en","primary_location":{"id":"doi:10.1137/25m1751347","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1751347","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2504.10091","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103065979","display_name":"Giacomo Borghi","orcid":"https://orcid.org/0000-0002-2478-807X"},"institutions":[{"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"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Giacomo Borghi","raw_affiliation_strings":["Maxwell Institute for Mathematical Sciences and Department of Mathematics, School of Mathematical and Computer Sciences (MACS), Heriot-Watt University, Edinburgh, EH14 4AP, UK"],"raw_orcid":"https://orcid.org/0000-0002-2478-807X","affiliations":[{"raw_affiliation_string":"Maxwell Institute for Mathematical Sciences and Department of Mathematics, School of Mathematical and Computer Sciences (MACS), Heriot-Watt University, Edinburgh, EH14 4AP, UK","institution_ids":["https://openalex.org/I4210117017"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009401094","display_name":"Lorenzo Pareschi","orcid":"https://orcid.org/0000-0002-8706-6939"},"institutions":[{"id":"https://openalex.org/I201324441","display_name":"University of Ferrara","ror":"https://ror.org/041zkgm14","country_code":"IT","type":"education","lineage":["https://openalex.org/I201324441"]},{"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"]}],"countries":["GB","IT"],"is_corresponding":false,"raw_author_name":"Lorenzo Pareschi","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Ferrara, Ferrara, 44121 Italy","Maxwell Institute for Mathematical Sciences and Department of Mathematics, School of Mathematical and Computer Sciences (MACS), Heriot-Watt University, Edinburgh, EH14 4AP, UK"],"raw_orcid":"https://orcid.org/0000-0002-8706-6939","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Ferrara, Ferrara, 44121 Italy","institution_ids":["https://openalex.org/I201324441"]},{"raw_affiliation_string":"Maxwell Institute for Mathematical Sciences and Department of Mathematics, School of Mathematical and Computer Sciences (MACS), Heriot-Watt University, Edinburgh, EH14 4AP, UK","institution_ids":["https://openalex.org/I4210117017"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02094704,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"64","issue":"2","first_page":"485","last_page":"509"},"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":0.9955999851226807,"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":0.9955999851226807,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9830999970436096,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9815999865531921,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/monte-carlo-method","display_name":"Monte Carlo method","score":0.7228000164031982},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5514000058174133},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.5224999785423279},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4659000039100647},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4505000114440918},{"id":"https://openalex.org/keywords/monte-carlo-molecular-modeling","display_name":"Monte Carlo molecular modeling","score":0.4196000099182129},{"id":"https://openalex.org/keywords/quasi-monte-carlo-method","display_name":"Quasi-Monte Carlo method","score":0.40880000591278076},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.4065000116825104},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.39590001106262207},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.3935999870300293}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.7228000164031982},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5817000269889832},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5742999911308289},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5644000172615051},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5514000058174133},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.5224999785423279},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4659000039100647},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4505000114440918},{"id":"https://openalex.org/C37669827","wikidata":"https://www.wikidata.org/wiki/Q6904703","display_name":"Monte Carlo molecular modeling","level":4,"score":0.4196000099182129},{"id":"https://openalex.org/C63320529","wikidata":"https://www.wikidata.org/wiki/Q7269435","display_name":"Quasi-Monte Carlo method","level":5,"score":0.40880000591278076},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.4065000116825104},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.39590001106262207},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3935999870300293},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.3894999921321869},{"id":"https://openalex.org/C45786274","wikidata":"https://www.wikidata.org/wiki/Q3333611","display_name":"Kinetic Monte Carlo","level":3,"score":0.3659000098705292},{"id":"https://openalex.org/C132725507","wikidata":"https://www.wikidata.org/wiki/Q39879","display_name":"Monte Carlo integration","level":5,"score":0.3628999888896942},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.3488999903202057},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.33709999918937683},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3334999978542328},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.32580000162124634},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.31929999589920044},{"id":"https://openalex.org/C122592724","wikidata":"https://www.wikidata.org/wiki/Q3855635","display_name":"Dynamic Monte Carlo method","level":3,"score":0.3156000077724457},{"id":"https://openalex.org/C204493344","wikidata":"https://www.wikidata.org/wiki/Q6904698","display_name":"Monte Carlo method in statistical physics","level":5,"score":0.31130000948905945},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C52421305","wikidata":"https://www.wikidata.org/wiki/Q1151499","display_name":"Particle filter","level":3,"score":0.2793999910354614},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C179003449","wikidata":"https://www.wikidata.org/wiki/Q1757458","display_name":"Particle system","level":2,"score":0.25940001010894775},{"id":"https://openalex.org/C57945734","wikidata":"https://www.wikidata.org/wiki/Q7977941","display_name":"Weak convergence","level":3,"score":0.2554999887943268},{"id":"https://openalex.org/C15482360","wikidata":"https://www.wikidata.org/wiki/Q15238499","display_name":"Monte Carlo algorithm","level":3,"score":0.2529999911785126},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.25130000710487366},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.25099998712539673}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/25m1751347","is_oa":false,"landing_page_url":"https://doi.org/10.1137/25m1751347","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2504.10091","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2504.10091","pdf_url":"https://arxiv.org/pdf/2504.10091","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,"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.2504.10091","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2504.10091","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2504.10091","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2504.10091","pdf_url":"https://arxiv.org/pdf/2504.10091","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,"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":[],"awards":[{"id":"https://openalex.org/G4508289328","display_name":null,"funder_award_id":"PE00000013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G731118236","display_name":null,"funder_award_id":"PE00000013","funder_id":"https://openalex.org/F4320321873","funder_display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320320006","display_name":"Royal Society","ror":"https://ror.org/03wnrjx87"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320321873","display_name":"Ministero dell\u2019Istruzione, dell\u2019Universit\u00e0 e della Ricerca","ror":"https://ror.org/0166hxq48"},{"id":"https://openalex.org/F4320334079","display_name":"Gruppo Nazionale per il Calcolo Scientifico","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4415159419.pdf","grobid_xml":"https://content.openalex.org/works/W4415159419.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0],"establish":[1],"quantitative":[2],"convergence":[3,88],"rates":[4],"for":[5,86,94],"stochastic":[6],"particle":[7,74],"approximation":[8],"based":[9],"on":[10],"Nanbu-type":[11],"Monte":[12,54,64,91],"Carlo":[13,55,65,92],"schemes":[14],"applied":[15],"to":[16,108],"a":[17,83,98,109],"broad":[18],"class":[19,111],"of":[20,46,90,106,112],"collisional":[21],"kinetic":[22],"models.":[23,48],"Using":[24],"coupling":[25],"techniques":[26],"and":[27,57,76,81,104],"stability":[28],"estimates":[29],"in":[30],"the":[31,42,47,70,87],"Wasserstein-1":[32],"(Kantorovich-Rubinstein)":[33],"metric,":[34],"we":[35,100],"derive":[36],"sharp":[37],"error":[38,79],"bounds":[39],"that":[40],"reflect":[41],"nonlinear":[43],"interaction":[44],"structure":[45],"Our":[49],"framework":[50],"includes":[51],"classical":[52],"Nanbu":[53],"method":[56],"more":[58],"recent":[59],"developments":[60],"as":[61],"Time":[62],"Relaxed":[63],"methods.":[66],"The":[67],"results":[68],"bridge":[69],"gap":[71],"between":[72],"probabilistic":[73],"approximations":[75],"deterministic":[77],"numerical":[78],"analysis,":[80],"provide":[82],"unified":[84],"perspective":[85],"theory":[89],"methods":[93],"Boltzmann-type":[95,113],"equations.":[96,114],"As":[97],"by-product,":[99],"also":[101],"obtain":[102],"existence":[103],"uniqueness":[105],"solutions":[107],"large":[110]},"counts_by_year":[],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-14T00:00:00"}