{"id":"https://openalex.org/W3023743705","doi":"https://doi.org/10.48550/arxiv.0810.0815","title":"Langevin Approach to Levy Flights in Fixed Potentials: Exact Results for Stationary Probability Distributions","display_name":"Langevin Approach to Levy Flights in Fixed Potentials: Exact Results for Stationary Probability Distributions","publication_year":2008,"publication_date":"2008-10-05","ids":{"openalex":"https://openalex.org/W3023743705","doi":"https://doi.org/10.48550/arxiv.0810.0815","mag":"3023743705"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:0810.0815","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0810.0815","pdf_url":"https://arxiv.org/pdf/0810.0815","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/0810.0815","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035764224","display_name":"Alexander A. Dubkov","orcid":"https://orcid.org/0000-0001-7443-0191","observed_orcids":["https://orcid.org/0000-0001-7443-0191"]},"institutions":[{"id":"https://openalex.org/I79563041","display_name":"N. I. Lobachevsky State University of Nizhny Novgorod","ror":"https://ror.org/01bb1zm18","country_code":"RU","type":"education","lineage":["https://openalex.org/I79563041"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Dubkov, A. A.","raw_affiliation_strings":["Radiophysics Department , Nizhni Novgorod State University 23 Gagarin Ave. , 603950 Nizhni Novgorod , Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Radiophysics Department , Nizhni Novgorod State University 23 Gagarin Ave. , 603950 Nizhni Novgorod , Russia","institution_ids":["https://openalex.org/I79563041"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057756312","display_name":"Bernardo Spagnolo","orcid":"https://orcid.org/0000-0002-6625-3989","observed_orcids":["https://orcid.org/0000-0002-6625-3989"]},"institutions":[{"id":"https://openalex.org/I4210115176","display_name":"National Interuniversity Consortium for the Physical Sciences of Matter","ror":"https://ror.org/026vvkz19","country_code":"IT","type":"nonprofit","lineage":["https://openalex.org/I4210115176"]},{"id":"https://openalex.org/I900890020","display_name":"University of Palermo","ror":"https://ror.org/044k9ta02","country_code":"IT","type":"education","lineage":["https://openalex.org/I900890020"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Spagnolo, B.","raw_affiliation_strings":["Dipartimento di Fisica e Tecnologie Relative , Universit\u00e0 di Palermo CNISM -Unit\u00e0 di Palermo , Group of Interdisciplinary Physics \u2021 Viale delle Scienze , I-90128 Palermo , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Fisica e Tecnologie Relative , Universit\u00e0 di Palermo CNISM -Unit\u00e0 di Palermo , Group of Interdisciplinary Physics \u2021 Viale delle Scienze , I-90128 Palermo , Italy","institution_ids":["https://openalex.org/I4210115176","https://openalex.org/I900890020"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":66,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"5","first_page":"1745","last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.8442000150680542,"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"}},"topics":[{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.8442000150680542,"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"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.14419999718666077,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11513","display_name":"stochastic dynamics and bifurcation","score":0.007600000128149986,"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/levy-flight","display_name":"L\u00e9vy flight","score":0.8130000233650208},{"id":"https://openalex.org/keywords/fractional-fokker-planck-equation","display_name":"fractional Fokker-Planck equation","score":0.9229999780654907},{"id":"https://openalex.org/keywords/langevin-equation","display_name":"Langevin equation","score":0.8849999904632568},{"id":"https://openalex.org/keywords/stationary-probability-density-function","display_name":"stationary probability density","score":0.7739999890327454},{"id":"https://openalex.org/keywords/superdiffusion","display_name":"superdiffusion","score":0.9259999990463257},{"id":"https://openalex.org/keywords/anharmonic-potential","display_name":"anharmonic potential","score":0.7519999742507935},{"id":"https://openalex.org/keywords/bimodal-distribution","display_name":"bimodal distribution","score":0.8619999885559082},{"id":"https://openalex.org/keywords/power-law-tails","display_name":"power-law tails","score":0.9940000176429749},{"id":"https://openalex.org/keywords/finite-variance","display_name":"finite variance","score":0.722000002861023},{"id":"https://openalex.org/keywords/functional-methods","display_name":"functional methods","score":0.8420000076293945}],"concepts":[{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.7142801284790039},{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.699249804019928},{"id":"https://openalex.org/C2777577648","wikidata":"https://www.wikidata.org/wiki/Q584537","display_name":"Langevin equation","level":2,"score":0.6522983312606812},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.6513242721557617},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.6070020198822021},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.5931495428085327},{"id":"https://openalex.org/C118918019","wikidata":"https://www.wikidata.org/wiki/Q4114998","display_name":"L\u00e9vy flight","level":3,"score":0.5540852546691895},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.5235105156898499},{"id":"https://openalex.org/C98951983","wikidata":"https://www.wikidata.org/wiki/Q7604341","display_name":"Stationary distribution","level":3,"score":0.5097126364707947},{"id":"https://openalex.org/C88757350","wikidata":"https://www.wikidata.org/wiki/Q1557613","display_name":"L\u00e9vy process","level":2,"score":0.4907754361629486},{"id":"https://openalex.org/C69123182","wikidata":"https://www.wikidata.org/wiki/Q891766","display_name":"Fokker\u2013Planck equation","level":3,"score":0.4650351405143738},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.4487702250480652},{"id":"https://openalex.org/C179709323","wikidata":"https://www.wikidata.org/wiki/Q1042429","display_name":"L\u00e9vy distribution","level":3,"score":0.4477425515651703},{"id":"https://openalex.org/C87040749","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Power law","level":2,"score":0.41674333810806274},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.41230645775794983},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29816436767578125},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.19882187247276306},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19275087118148804},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16378659009933472},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1539667248725891},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1268807351589203},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.12626862525939941},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:0810.0815","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0810.0815","pdf_url":"https://arxiv.org/pdf/0810.0815","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.0810.0815","doi":"https://doi.org/10.48550/arxiv.0810.0815","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0810.0815","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":"article-journal"},{"id":"mag:3023743705","doi":null,"is_oa":false,"landing_page_url":"http://ui.adsabs.harvard.edu/abs/2007AcPPB..38.1745D/abstract","pdf_url":null,"source":{"id":"https://openalex.org/S131967590","display_name":"Acta Physica Polonica B","issn_l":"0587-4254","issn":["0587-4254","1509-5770"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310317381","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/P4310317381"],"host_organization_lineage_names":["Jagiellonian University"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Acta Physica Polonica B","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0810.0815","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0810.0815","pdf_url":"https://arxiv.org/pdf/0810.0815","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3023743705.pdf","grobid_xml":"https://content.openalex.org/works/W3023743705.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W1665258060","https://openalex.org/W2751862591"],"related_works":["https://openalex.org/W6992197339","https://openalex.org/W2078671468","https://openalex.org/W2400030893","https://openalex.org/W2054386976","https://openalex.org/W7048644786","https://openalex.org/W1994073355","https://openalex.org/W2144426929","https://openalex.org/W2030897788","https://openalex.org/W2062100544","https://openalex.org/W3042671472"],"abstract_inverted_index":{"The":[0,66],"functional":[1],"method":[2],"to":[3],"derive":[4],"the":[5,13,23,29,47,50,60,78,88],"fractional":[6],"Fokker-Planck":[7],"equation":[8,15],"for":[9,58],"probability":[10,32,68],"distribution":[11,57],"from":[12],"Langevin":[14],"with":[16,53,95],"Levy":[17,36,91],"stable":[18,25],"noise":[19,26],"is":[20],"proposed.":[21],"For":[22],"Cauchy":[24],"we":[27],"obtain":[28],"exact":[30],"stationary":[31,56,67],"density":[33,69],"function":[34],"of":[35,46,77,90],"flights":[37,92],"in":[38,49,93],"different":[39],"smooth":[40],"potential":[41],"profiles.":[42],"We":[43],"find":[44],"confinement":[45],"particle":[48],"superdiffusion":[51],"motion":[52,98],"a":[54],"bimodal":[55],"all":[59],"anharmonic":[61],"symmetric":[62],"monostable":[63],"potentials":[64],"investigated.":[65],"functions":[70],"show":[71],"power-law":[72],"tails,":[73],"which":[74],"ensure":[75],"finiteness":[76],"variance.":[79],"By":[80],"reviewing":[81],"recent":[82],"results":[83],"on":[84],"these":[85],"statistical":[86],"characteristics,":[87],"peculiarities":[89],"comparison":[94],"ordinary":[96],"Brownian":[97],"are":[99],"discussed.":[100]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2020-05-13T00:00:00"}
