{"id":"https://openalex.org/W7204943468","doi":"https://doi.org/10.48550/arxiv.2608.30493","title":"McKean-Vlasov Differential Equations: An introduction and a focus on some kinetic models","display_name":"McKean-Vlasov Differential Equations: An introduction and a focus on some kinetic models","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204943468","doi":"https://doi.org/10.48550/arxiv.2608.30493"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30493","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30493","pdf_url":"https://arxiv.org/pdf/2608.30493","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.30493","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001028268","display_name":"Stefano Pagliarani","orcid":"https://orcid.org/0000-0003-4329-7054","observed_orcids":["https://orcid.org/0000-0003-4329-7054"]},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Pagliarani, Stefano","raw_affiliation_strings":["Dipartimento di Matematica , Universit\u00e0 di Bologna , Bologna , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica , Universit\u00e0 di Bologna , Bologna , Italy","institution_ids":["https://openalex.org/I9360294"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5001028268"],"corresponding_institution_ids":["https://openalex.org/I9360294"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.8877000212669373,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.8877000212669373,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.06369999796152115,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.01810000091791153,"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/mckean-vlasov-stochastic-differential-equations","display_name":"McKean-Vlasov stochastic differential equations","score":0.9900000095367432},{"id":"https://openalex.org/keywords/mean-field-interacting-particle-systems","display_name":"mean-field interacting particle systems","score":0.9950000047683716},{"id":"https://openalex.org/keywords/degenerate-noise","display_name":"degenerate noise","score":0.9990000128746033},{"id":"https://openalex.org/keywords/non-euclidean-geometry","display_name":"non-Euclidean geometry","score":0.9860000014305115},{"id":"https://openalex.org/keywords/well-posedness","display_name":"well-posedness","score":0.9620000123977661},{"id":"https://openalex.org/keywords/regularity-estimates","display_name":"regularity estimates","score":0.7160000205039978},{"id":"https://openalex.org/keywords/schauder-estimates","display_name":"Schauder estimates","score":0.9890000224113464},{"id":"https://openalex.org/keywords/superposition","display_name":"superposition","score":0.9309999942779541}],"concepts":[{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.6977999806404114},{"id":"https://openalex.org/C27753989","wikidata":"https://www.wikidata.org/wiki/Q284885","display_name":"Superposition principle","level":2,"score":0.5609999895095825},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5335999727249146},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5303999781608582},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5235000252723694},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.48510000109672546},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.4713999927043915},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4571000039577484},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4327999949455261},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4041999876499176},{"id":"https://openalex.org/C85725439","wikidata":"https://www.wikidata.org/wiki/Q466686","display_name":"Anisotropy","level":2,"score":0.3626999855041504},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36230000853538513},{"id":"https://openalex.org/C135889238","wikidata":"https://www.wikidata.org/wiki/Q46276","display_name":"Kinetic energy","level":2,"score":0.33160001039505005},{"id":"https://openalex.org/C2778517922","wikidata":"https://www.wikidata.org/wiki/Q7140482","display_name":"Particle (ecology)","level":2,"score":0.3174999952316284},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.30329999327659607},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29269999265670776},{"id":"https://openalex.org/C179003449","wikidata":"https://www.wikidata.org/wiki/Q1757458","display_name":"Particle system","level":2,"score":0.28870001435279846},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.26969999074935913},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.26269999146461487}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30493","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30493","pdf_url":"https://arxiv.org/pdf/2608.30493","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":"doi:10.48550/arxiv.2608.30493","doi":"https://doi.org/10.48550/arxiv.2608.30493","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30493","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":"pmh:oai:arXiv.org:2608.30493","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30493","pdf_url":"https://arxiv.org/pdf/2608.30493","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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204943468.pdf","grobid_xml":"https://content.openalex.org/works/W7204943468.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4399725671","https://openalex.org/W4399725656","https://openalex.org/W4403570159","https://openalex.org/W4406733673","https://openalex.org/W4401437345","https://openalex.org/W4287865407","https://openalex.org/W7096468370","https://openalex.org/W3196783561","https://openalex.org/W4226080473","https://openalex.org/W4406213729"],"abstract_inverted_index":{"These":[0],"notes":[1],"were":[2],"prepared":[3],"for":[4],"a":[5],"series":[6],"of":[7],"lectures":[8],"delivered":[9],"at":[10],"the":[11,66,70,75],"43rd":[12],"Finnish":[13],"Summer":[14],"School":[15],"on":[16,89],"Probability":[17],"and":[18,39,46,58,74,78,82,85,92],"Statistics,":[19],"held":[20],"in":[21],"Lammi,":[22],"Finland,":[23],"from":[24],"May":[25],"26":[26],"to":[27,34,55,59],"30,":[28],"2025.":[29],"They":[30],"provide":[31],"an":[32],"introduction":[33],"McKean-Vlasov":[35],"stochastic":[36],"differential":[37],"equations":[38,45,57],"their":[40],"connections":[41],"with":[42,62],"non-linear":[43],"Fokker-Planck":[44],"mean-field":[47],"interacting":[48],"particle":[49],"systems.":[50],"Particular":[51],"attention":[52],"is":[53],"devoted":[54],"density-dependent":[56],"kinetic-type":[60],"models":[61],"degenerate":[63],"noise.":[64],"For":[65],"latter,":[67],"we":[68],"introduce":[69],"underlying":[71],"non-Euclidean":[72],"geometry":[73],"associated":[76],"anisotropic":[77],"intrinsic":[79],"H\u00f6lder":[80],"spaces,":[81],"present":[83],"well-posedness":[84],"regularity":[86],"results":[87],"based":[88],"Schauder":[90],"estimates":[91],"superposition":[93],"principles.":[94]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-02T00:00:00"}