{"id":"https://openalex.org/W7212002069","doi":"https://doi.org/10.48550/arxiv.2609.07622","title":"On the stationary measures of the critical Ornstein--Uhlenbeck process","display_name":"On the stationary measures of the critical Ornstein--Uhlenbeck process","publication_year":2026,"publication_date":"2026-09-07","ids":{"openalex":"https://openalex.org/W7212002069","doi":"https://doi.org/10.48550/arxiv.2609.07622"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.07622","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07622","pdf_url":"https://arxiv.org/pdf/2609.07622","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/2609.07622","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103082092","display_name":"Jean\u2010Dominique Deuschel","orcid":"https://orcid.org/0000-0003-0953-5776","observed_orcids":["https://orcid.org/0000-0003-0953-5776"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Deuschel, Jean-Dominique","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085532662","display_name":"Jonas K\u00f6ppl","orcid":"https://orcid.org/0000-0001-9188-1883","observed_orcids":["https://orcid.org/0000-0001-9188-1883"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K\u00f6ppl, Jonas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114316429","display_name":"Yannic Steenbeck","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Steenbeck, Yannic","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5020298678","display_name":"Thomas Worschech","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Worschech, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9926999807357788,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9926999807357788,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.002199999988079071,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.002199999988079071,"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/ornstein-uhlenbeck-process","display_name":"Ornstein-Uhlenbeck process","score":0.8999999761581421},{"id":"https://openalex.org/keywords/stationary-measures","display_name":"stationary measures","score":0.9570000171661377},{"id":"https://openalex.org/keywords/reversible-measures","display_name":"reversible measures","score":0.6169999837875366},{"id":"https://openalex.org/keywords/harmonic-crystal","display_name":"harmonic crystal","score":0.7009999752044678},{"id":"https://openalex.org/keywords/langevin-dynamics","display_name":"Langevin dynamics","score":0.8270000219345093},{"id":"https://openalex.org/keywords/conductance","display_name":"conductance","score":0.4740000069141388},{"id":"https://openalex.org/keywords/random-conductances","display_name":"random conductances","score":0.7360000014305115},{"id":"https://openalex.org/keywords/spectral-analysis","display_name":"spectral analysis","score":0.6259999871253967}],"concepts":[{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6304000020027161},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5896999835968018},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.5690000057220459},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.5412999987602234},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5185999870300293},{"id":"https://openalex.org/C110405555","wikidata":"https://www.wikidata.org/wiki/Q1192209","display_name":"Stationary process","level":2,"score":0.48750001192092896},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4846000075340271},{"id":"https://openalex.org/C47458137","wikidata":"https://www.wikidata.org/wiki/Q911951","display_name":"Stationary state","level":2,"score":0.48249998688697815},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.4661000072956085},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.4564000070095062},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.39309999346733093},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.3720000088214874},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.3612000048160553},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3131999969482422},{"id":"https://openalex.org/C168110828","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral density","level":2,"score":0.3125},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.30379998683929443},{"id":"https://openalex.org/C2988492214","wikidata":"https://www.wikidata.org/wiki/Q911951","display_name":"Stationary solution","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.2955000102519989},{"id":"https://openalex.org/C18436578","wikidata":"https://www.wikidata.org/wiki/Q7604346","display_name":"Stationary sequence","level":3,"score":0.28679999709129333},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.27900001406669617},{"id":"https://openalex.org/C61062188","wikidata":"https://www.wikidata.org/wiki/Q835065","display_name":"Second moment of area","level":2,"score":0.2734000086784363},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.26829999685287476},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.2646999955177307},{"id":"https://openalex.org/C68710425","wikidata":"https://www.wikidata.org/wiki/Q5275442","display_name":"Diffusion process","level":3,"score":0.2628999948501587}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.07622","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07622","pdf_url":"https://arxiv.org/pdf/2609.07622","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.2609.07622","doi":"https://doi.org/10.48550/arxiv.2609.07622","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.07622","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-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.07622","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.07622","pdf_url":"https://arxiv.org/pdf/2609.07622","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":[{"id":"https://openalex.org/F4320334763","display_name":"Leibniz-Gemeinschaft","ror":"https://ror.org/01n6r0e97"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212002069.pdf","grobid_xml":"https://content.openalex.org/works/W7212002069.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W1422901211","https://openalex.org/W1511623908","https://openalex.org/W1547924129","https://openalex.org/W1649209399","https://openalex.org/W1923692825","https://openalex.org/W1967237126","https://openalex.org/W1971737366","https://openalex.org/W2010141788","https://openalex.org/W2015651405","https://openalex.org/W2025952466","https://openalex.org/W2035881626","https://openalex.org/W2048863976","https://openalex.org/W2049322374","https://openalex.org/W2055151739","https://openalex.org/W2057881547","https://openalex.org/W2078096403","https://openalex.org/W2086317761","https://openalex.org/W2090537713","https://openalex.org/W2143251517","https://openalex.org/W2474752352","https://openalex.org/W2765846489","https://openalex.org/W2963316340","https://openalex.org/W3129854827","https://openalex.org/W3210004527","https://openalex.org/W4221160309","https://openalex.org/W4389342257","https://openalex.org/W4402236441","https://openalex.org/W4408373478","https://openalex.org/W4408717990","https://openalex.org/W4414295105","https://openalex.org/W7131701971","https://openalex.org/W7140197484"],"related_works":["https://openalex.org/W2120436883","https://openalex.org/W2086280413","https://openalex.org/W2074248079","https://openalex.org/W3043328677","https://openalex.org/W2326122831","https://openalex.org/W2946119151","https://openalex.org/W200200593","https://openalex.org/W4293323172","https://openalex.org/W2942950398","https://openalex.org/W4415533602"],"abstract_inverted_index":{"We":[0,71],"study":[1,127],"linear":[2,99],"and":[3,80,89,107],"symmetric":[4],"diffusion":[5],"processes":[6],"on":[7,29,47,61],"$\\mathbb{R}^{\\mathbb{Z}^d}$":[8],"that":[9,65,97],"can":[10,101],"be":[11],"seen":[12],"as":[13],"the":[14,18,34,37,48,52,62,98,113,129],"Langevin":[15],"dynamics":[16],"of":[17,36,44,112,115,120,128,131],"(inhomogeneous)":[19],"harmonic":[20],"crystal":[21],"for":[22,75],"given":[23],"conductances,":[24],"with":[25],"a":[26,41,109,126],"particular":[27],"focus":[28],"their":[30],"stationary":[31,67,84,91],"distributions.":[32],"Despite":[33],"linearity":[35],"interaction,":[38],"we":[39,95],"exhibit":[40,103],"rich":[42],"variety":[43],"behaviours,":[45],"depending":[46],"disorder":[49],"encoded":[50],"by":[51,125],"conductances.":[53],"Our":[54],"main":[55],"results":[56],"provide":[57,73,108],"essentially":[58],"sharp":[59],"criteria":[60,78],"conductances":[63,122,133],"ensuring":[64],"every":[66],"measure":[68],"is":[69,123],"reversible.":[70],"also":[72],"examples":[74],"which":[76],"these":[77],"fail":[79],"where":[81],"either":[82],"no":[83],"measures":[85,92],"exist":[86],"or":[87],"reversible":[88],"non-reversible":[90],"coexist.":[93],"Additionally,":[94],"show":[96],"system":[100],"even":[102],"non-trivial":[104],"time-periodic":[105],"behaviour":[106],"spectral":[110],"characterisation":[111],"occurrence":[114],"such":[116],"oscillations.":[117],"The":[118],"case":[119,130],"deterministic":[121],"complemented":[124],"random":[132],"under":[134],"quite":[135],"general":[136],"moment":[137],"assumptions.":[138]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-10T00:00:00"}