{"id":"https://openalex.org/W2557080614","doi":"https://doi.org/10.1137/16m1103816","title":"Spectral Theory for Random Poincar\u00e9 Maps","display_name":"Spectral Theory for Random Poincar\u00e9 Maps","publication_year":2017,"publication_date":"2017-01-01","ids":{"openalex":"https://openalex.org/W2557080614","doi":"https://doi.org/10.1137/16m1103816","mag":"2557080614"},"language":"en","primary_location":{"id":"doi:10.1137/16m1103816","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1103816","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1611.04869","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Manon Baudel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Manon Baudel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Nils Berglund","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nils Berglund","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":0.3047,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.60770297,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"49","issue":"6","first_page":"4319","last_page":"4375"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9980000257492065,"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":0.9980000257492065,"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":0.9976000189781189,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7269999980926514},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.6897000074386597},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.5083000063896179},{"id":"https://openalex.org/keywords/spectral-theory","display_name":"Spectral theory","score":0.5022000074386597},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.46889999508857727},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.4117000102996826},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.40630000829696655},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.373199999332428},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3662000000476837}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8999999761581421},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7269999980926514},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.6897000074386597},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5698000192642212},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.5083000063896179},{"id":"https://openalex.org/C98306654","wikidata":"https://www.wikidata.org/wiki/Q2409122","display_name":"Spectral theory","level":3,"score":0.5022000074386597},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.46889999508857727},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4117000102996826},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.40630000829696655},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.373199999332428},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3662000000476837},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.366100013256073},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.36090001463890076},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.3352999985218048},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.334199994802475},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C186121230","wikidata":"https://www.wikidata.org/wiki/Q7575215","display_name":"Spectral theory of ordinary differential equations","level":5,"score":0.32359999418258667},{"id":"https://openalex.org/C105671362","wikidata":"https://www.wikidata.org/wiki/Q6787870","display_name":"Matrix differential equation","level":3,"score":0.32280001044273376},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.32179999351501465},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.30160000920295715},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.290800005197525},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.2906000018119812},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.26809999346733093},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.26260000467300415}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/16m1103816","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1103816","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1611.04869","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.04869","pdf_url":"https://arxiv.org/pdf/1611.04869","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":"pmh:oai:HAL:hal-01397184v2","is_oa":false,"landing_page_url":"https://hal.science/hal-01397184","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://epubs.siam.org/doi/pdf/10.1137/16M1103816","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1611.04869","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.04869","pdf_url":"https://arxiv.org/pdf/1611.04869","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W150579876","https://openalex.org/W1966554843","https://openalex.org/W1968548276","https://openalex.org/W1978065031","https://openalex.org/W2002610056","https://openalex.org/W2004018226","https://openalex.org/W2021290840","https://openalex.org/W2028385516","https://openalex.org/W2031843459","https://openalex.org/W2037190719","https://openalex.org/W2037393162","https://openalex.org/W2053391349","https://openalex.org/W2064319030","https://openalex.org/W2084449024","https://openalex.org/W2084927133","https://openalex.org/W2085375591","https://openalex.org/W2092211891","https://openalex.org/W2093915651","https://openalex.org/W2095478218","https://openalex.org/W2117475827","https://openalex.org/W2151822821","https://openalex.org/W2161721539","https://openalex.org/W2163272743","https://openalex.org/W2208541893","https://openalex.org/W2328226763","https://openalex.org/W2382119871","https://openalex.org/W2388048240","https://openalex.org/W2473330746","https://openalex.org/W2963132702"],"related_works":[],"abstract_inverted_index":{"We":[0,22,42],"consider":[1],"stochastic":[2],"differential":[3,14],"equations,":[4],"obtained":[5],"by":[6,86,124],"adding":[7],"weak":[8],"Gaussian":[9],"white":[10],"noise":[11],"to":[12,55],"ordinary":[13],"equations":[15],"admitting":[16],"$N$":[17,49],"asymptotically":[18],"stable":[19],"periodic":[20,78],"orbits.":[21,79],"construct":[23],"a":[24,30,118],"discrete-time,":[25],"continuous-space":[26],"Markov":[27],"chain,":[28],"called":[29],"random":[31],"Poincar\u00e9":[32],"map,":[33],"which":[34,51],"encodes":[35],"the":[36,40],"metastable":[37],"behavior":[38],"of":[39,72,75,77,92,98,114],"system.":[41],"show":[43],"that":[44],"this":[45],"process":[46],"admits":[47],"exactly":[48],"eigenvalues":[50,63,81,88],"are":[52,84],"exponentially":[53],"close":[54],"$1$,":[56],"and":[57,64,67,82,89,117],"we":[58],"provide":[59],"expressions":[60],"for":[61,108],"these":[62,99],"their":[65],"left":[66],"right":[68],"eigenfunctions":[69,83],"in":[70],"terms":[71],"committor":[73,125],"functions":[74],"neighborhoods":[76],"The":[80,101],"well-approximated":[85],"principal":[87],"quasi-stationary":[90],"distributions":[91],"processes":[93],"killed":[94],"upon":[95],"hitting":[96],"some":[97],"neighborhoods.":[100],"proofs":[102],"rely":[103],"on":[104],"Feynman--Kac-type":[105],"representation":[106],"formulas":[107],"eigenfunctions,":[109],"Doob's":[110],"$h$-transform,":[111],"spectral":[112],"theory":[113],"compact":[115],"operators,":[116],"recently":[119],"discovered":[120],"detailed-balance":[121],"property":[122],"satisfied":[123],"functions.":[126]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2016-11-30T00:00:00"}