{"id":"https://openalex.org/W7214186990","doi":"https://doi.org/10.48550/arxiv.2609.28338","title":"Local Geometric Mixing via Dobrushin Contraction with Applications to Diffusion Path Monte Carlo and the Proximal Sampler","display_name":"Local Geometric Mixing via Dobrushin Contraction with Applications to Diffusion Path Monte Carlo and the Proximal Sampler","publication_year":2026,"publication_date":"2026-09-23","ids":{"openalex":"https://openalex.org/W7214186990","doi":"https://doi.org/10.48550/arxiv.2609.28338"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.28338","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28338","pdf_url":"https://arxiv.org/pdf/2609.28338","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/2609.28338","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092796546","display_name":"Stefan Oberd\u00f6rster","orcid":"https://orcid.org/0009-0004-0734-0101","observed_orcids":["https://orcid.org/0009-0004-0734-0101"]},"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"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Oberd\u00f6rster, Stefan","raw_affiliation_strings":["Institute for Applied Mathematics , University of Bonn"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Applied Mathematics , University of Bonn","institution_ids":["https://openalex.org/I135140700"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5092796546"],"corresponding_institution_ids":["https://openalex.org/I135140700"],"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":1.0,"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":1.0,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.0,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.0,"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/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.8859999775886536},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"spectral gap","score":0.6940000057220459},{"id":"https://openalex.org/keywords/total-variation-convergence","display_name":"total variation convergence","score":0.7319999933242798}],"concepts":[{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.7957000136375427},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.6414999961853027},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.593500018119812},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.576200008392334},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5741999745368958},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5320000052452087},{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.47620001435279846},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4693000018596649},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.4284999966621399},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.4041000008583069},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.3806999921798706},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.37380000948905945},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.33719998598098755},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.3330000042915344},{"id":"https://openalex.org/C104065381","wikidata":"https://www.wikidata.org/wiki/Q1002535","display_name":"Geometric modeling","level":2,"score":0.2793000042438507},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.275299996137619},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27489998936653137},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.25999999046325684},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2563000023365021},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.2547000050544739}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.28338","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28338","pdf_url":"https://arxiv.org/pdf/2609.28338","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.2609.28338","doi":"https://doi.org/10.48550/arxiv.2609.28338","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.28338","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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.28338","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28338","pdf_url":"https://arxiv.org/pdf/2609.28338","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":[{"id":"https://openalex.org/G5686947098","display_name":null,"funder_award_id":"539309657","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8265043617","display_name":null,"funder_award_id":"CRC 1720","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214186990.pdf","grobid_xml":"https://content.openalex.org/works/W7214186990.grobid-xml"},"referenced_works_count":45,"referenced_works":["https://openalex.org/W88155604","https://openalex.org/W140231913","https://openalex.org/W288172476","https://openalex.org/W1573820523","https://openalex.org/W1600293573","https://openalex.org/W1965880646","https://openalex.org/W1972988517","https://openalex.org/W1974469893","https://openalex.org/W1975257745","https://openalex.org/W1983452151","https://openalex.org/W1986613495","https://openalex.org/W1991111872","https://openalex.org/W2040060987","https://openalex.org/W2056452850","https://openalex.org/W2064975486","https://openalex.org/W2067708435","https://openalex.org/W2071048859","https://openalex.org/W2076430891","https://openalex.org/W2087667141","https://openalex.org/W2114964853","https://openalex.org/W2128669232","https://openalex.org/W2138309709","https://openalex.org/W2153840565","https://openalex.org/W2159000620","https://openalex.org/W2162898443","https://openalex.org/W2312245927","https://openalex.org/W2542623543","https://openalex.org/W3155914913","https://openalex.org/W3193980422","https://openalex.org/W3201118272","https://openalex.org/W4205537960","https://openalex.org/W4226192527","https://openalex.org/W4233762729","https://openalex.org/W4302617909","https://openalex.org/W4317815220","https://openalex.org/W4353080673","https://openalex.org/W4393002334","https://openalex.org/W4399856132","https://openalex.org/W4416675279","https://openalex.org/W7127396172","https://openalex.org/W7134855328","https://openalex.org/W7140123237","https://openalex.org/W7168302245","https://openalex.org/W7171523233","https://openalex.org/W7206170707"],"related_works":["https://openalex.org/W7163443385","https://openalex.org/W7100371170","https://openalex.org/W2078038392","https://openalex.org/W2265232045","https://openalex.org/W7166561747","https://openalex.org/W4403571205","https://openalex.org/W2136521556","https://openalex.org/W3102676823","https://openalex.org/W3099089001","https://openalex.org/W2472802697"],"abstract_inverted_index":{"Local":[0],"geometric":[1,4,8,42],"mixing":[2,5,33,43,96,116],"localizes":[3],"by":[6],"requiring":[7],"convergence":[9,23],"to":[10,53],"equilibrium":[11],"in":[12,70],"total":[13],"variation":[14],"only":[15],"over":[16],"finitely":[17],"many":[18],"transitions.":[19],"It":[20],"accommodates":[21],"local":[22,28,41],"rates":[24],"and":[25,39,90],"captures":[26],"rapid":[27],"equilibration,":[29],"even":[30],"when":[31],"global":[32],"is":[34],"much":[35],"slower.":[36],"We":[37,48],"establish":[38],"discuss":[40],"bounds":[44],"through":[45],"Dobrushin":[46],"contraction.":[47],"then":[49],"apply":[50],"this":[51],"approach":[52],"Diffusion":[54],"Path":[55],"Monte":[56,63],"Carlo,":[57],"a":[58],"recently":[59],"proposed":[60],"Markov":[61],"chain":[62],"Carlo":[64],"method,":[65,104],"aimed":[66],"at":[67],"leveraging":[68],"advances":[69],"score-based":[71],"modeling,":[72],"whose":[73],"ideal":[74,88,103],"transitions":[75],"coincide":[76],"with":[77],"those":[78],"of":[79],"the":[80,87,102],"Proximal":[81],"Sampler.":[82],"Our":[83],"analysis":[84],"covers":[85],"both":[86],"method":[89],"its":[91],"implementable":[92],"Metropolis-adjusted":[93],"counterpart,":[94],"providing":[95],"guarantees":[97,106],"under":[98],"minimal":[99],"assumptions.":[100],"For":[101],"these":[105],"complement":[107],"recent":[108],"spectral":[109],"gap":[110],"estimates,":[111],"which":[112],"we":[113],"develop":[114],"into":[115],"time":[117],"bounds.":[118]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-25T00:00:00"}