{"id":"https://openalex.org/W7223601916","doi":"https://doi.org/10.48550/arxiv.2610.32829","title":"The Two-Dimensional Narrow Escape Problem with Deterministic Initial Condition: Mean Escape Time and Escape location probabilities","display_name":"The Two-Dimensional Narrow Escape Problem with Deterministic Initial Condition: Mean Escape Time and Escape location probabilities","publication_year":2026,"publication_date":"2026-10-23","ids":{"openalex":"https://openalex.org/W7223601916","doi":"https://doi.org/10.48550/arxiv.2610.32829"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.32829","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32829","pdf_url":"https://arxiv.org/pdf/2610.32829","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/2610.32829","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093685403","display_name":"Lo\u00efs Delande","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210146074","display_name":"Analyse, G\u00e9om\u00e9trie et Mod\u00e9lisation","ror":"https://ror.org/03qgt2624","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210142324","https://openalex.org/I4210146074"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Delande, Lo\u00efs","raw_affiliation_strings":["AGM - UMR 8088"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AGM - UMR 8088","institution_ids":["https://openalex.org/I4210146074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048560398","display_name":"Tony Leli\u00e8vre A","orcid":"https://orcid.org/0000-0002-3412-113X","observed_orcids":["https://orcid.org/0000-0002-3412-113X"]},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Leli\u00e8vre, Tony","raw_affiliation_strings":["CERMICS"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CERMICS","institution_ids":["https://openalex.org/I4210128309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077185209","display_name":"Boris Nectoux","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nectoux, Boris","raw_affiliation_strings":["LMBP"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LMBP","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010543373","display_name":"Thomas Normand","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Normand, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.43549999594688416,"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":0.43549999594688416,"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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.09220000356435776,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.0877000018954277,"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/narrow-escape-problem","display_name":"narrow escape problem","score":0.9769999980926514},{"id":"https://openalex.org/keywords/brownian-motion","display_name":"Brownian motion","score":0.7639999985694885},{"id":"https://openalex.org/keywords/mean-escape-time","display_name":"mean escape time","score":0.9430000185966492},{"id":"https://openalex.org/keywords/asymptotic-analysis","display_name":"asymptotic analysis","score":0.8230000138282776},{"id":"https://openalex.org/keywords/mixed-boundary-value-problem","display_name":"mixed boundary value problem","score":0.9309999942779541},{"id":"https://openalex.org/keywords/maximal-regularity","display_name":"maximal regularity","score":0.8109999895095825},{"id":"https://openalex.org/keywords/two-dimensional-diffusion","display_name":"two-dimensional diffusion","score":0.6570000052452087}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6284999847412109},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.6103000044822693},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5189999938011169},{"id":"https://openalex.org/C2778751112","wikidata":"https://www.wikidata.org/wiki/Q835016","display_name":"Window (computing)","level":2,"score":0.4447000026702881},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.43630000948905945},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.41999998688697815},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.41179999709129333},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.41119998693466187},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.39980000257492065},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3971000015735626},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.39250001311302185},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3734999895095825},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.34769999980926514},{"id":"https://openalex.org/C2778738651","wikidata":"https://www.wikidata.org/wiki/Q16546687","display_name":"Novelty","level":2,"score":0.3391000032424927},{"id":"https://openalex.org/C75438885","wikidata":"https://www.wikidata.org/wiki/Q3403615","display_name":"Large deviations theory","level":2,"score":0.3285999894142151},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.3255000114440918},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.3165999948978424},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.295199990272522},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.28529998660087585},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.27970001101493835},{"id":"https://openalex.org/C186659197","wikidata":"https://www.wikidata.org/wiki/Q5452195","display_name":"First-hitting-time model","level":2,"score":0.2784000039100647},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.2621000111103058},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.26089999079704285}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2610.32829","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32829","pdf_url":"https://arxiv.org/pdf/2610.32829","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":"pmh:oai:HAL:hal-05836546v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-05836546","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2026","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.2610.32829","doi":"https://doi.org/10.48550/arxiv.2610.32829","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.32829","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:2610.32829","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.32829","pdf_url":"https://arxiv.org/pdf/2610.32829","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/G3129560191","display_name":"Longtime of Stochastic Dynamical Systems","funder_award_id":"ANR-25-CE40-6875","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223601916.pdf","grobid_xml":"https://content.openalex.org/works/W7223601916.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4390961238","https://openalex.org/W4391555658"],"related_works":["https://openalex.org/W2281421146","https://openalex.org/W2041034952","https://openalex.org/W7196957595","https://openalex.org/W2952515679","https://openalex.org/W2917848577","https://openalex.org/W4389118827","https://openalex.org/W2336411034","https://openalex.org/W2012392664","https://openalex.org/W1988744409","https://openalex.org/W7097949837"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,14,19,120,178],"rigorous":[4,107],"asymptotic":[5,39,45,181],"analysis":[6],"of":[7,37,51,59,93,102,109,119,136,139,142,153,160,162],"the":[8,26,30,38,49,52,56,60,64,72,76,106,110,117,124,133,137,140,150,157,166],"two-dimensional":[9],"narrow":[10],"escape":[11,28,40,53,125,167],"problem":[12],"for":[13,183],"Brownian":[15],"particle":[16],"initiated":[17],"at":[18,123,165,189],"deterministic":[20],"position":[21,74],"x.":[22],"While":[23],"we":[24,148,171],"address":[25],"mean":[27],"time,":[29],"main":[31],"novelty":[32],"lies":[33],"in":[34,116],"our":[35,154],"derivation":[36],"distribution.":[41],"We":[42],"derive":[43],"explicit":[44],"formulas":[46,85],"that":[47],"characterize":[48],"dependence":[50],"behavior":[54],"on":[55,132],"relative":[57,191],"configuration":[58],"starting":[61,73],"point":[62],"and":[63,79],"window":[65,126,168,186],"centers.":[66],"These":[67],"results":[68,131,175],"remain":[69],"valid":[70],"as":[71],"approaches":[75],"boundary":[77,113,145],"windows":[78],"include":[80],"refined":[81],"error":[82],"estimates.":[83],"The":[84],"are":[86],"obtained":[87],"with":[88],"two":[89],"independent":[90],"methods,":[91],"each":[92],"them":[94],"having":[95],"their":[96],"own":[97],"interest.":[98],"A":[99],"central":[100],"feature":[101],"this":[103],"work":[104],"is":[105],"treatment":[108],"underlying":[111],"mixed":[112,144],"value":[114,146],"problems":[115],"absence":[118],"contact":[121],"angle":[122],"boundaries.":[127,169],"By":[128],"leveraging":[129],"recent":[130],"maximal":[134],"regularity":[135,161],"gradient":[138],"solutions":[141,164],"such":[143],"problems,":[147],"ensure":[149],"analytical":[151],"validity":[152],"approach":[155],"despite":[156],"inherent":[158],"loss":[159],"these":[163,173],"Finally,":[170],"apply":[172],"general":[174],"to":[176],"provide":[177],"full":[179],"sharp":[180],"equivalents":[182],"regimes":[184],"where":[185],"sizes":[187],"scale":[188],"specific":[190],"rates.":[192]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-26T00:00:00"}
