{"id":"https://openalex.org/W31910362","doi":"https://doi.org/10.4169/000298910x480072","title":"P\u00f3lya\u2019s Theorem on Random Walks via P\u00f3lya\u2019s Urn","display_name":"P\u00f3lya\u2019s Theorem on Random Walks via P\u00f3lya\u2019s Urn","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W31910362","doi":"https://doi.org/10.4169/000298910x480072","mag":"31910362"},"language":"en","primary_location":{"id":"doi:10.4169/000298910x480072","is_oa":false,"landing_page_url":"https://doi.org/10.4169/000298910x480072","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065857248","display_name":"David Levin","orcid":"https://orcid.org/0000-0003-1103-6394"},"institutions":[{"id":"https://openalex.org/I181233156","display_name":"University of Oregon","ror":"https://ror.org/0293rh119","country_code":"US","type":"education","lineage":["https://openalex.org/I181233156"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"David A. Levin","raw_affiliation_strings":["Department of Mathematics, University of Oregon, Eugene, Oregon97402-1222\u00a0","Department of Mathematics, University of Oregon, Eugene, Oregon97402-1222"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Oregon, Eugene, Oregon97402-1222\u00a0","institution_ids":["https://openalex.org/I181233156"]},{"raw_affiliation_string":"Department of Mathematics, University of Oregon, Eugene, Oregon97402-1222","institution_ids":["https://openalex.org/I181233156"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020836845","display_name":"Yuval Peres","orcid":"https://orcid.org/0000-0001-5456-6323"},"institutions":[{"id":"https://openalex.org/I4210164937","display_name":"Microsoft Research (United Kingdom)","ror":"https://ror.org/05k87vq12","country_code":"GB","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]},{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]}],"countries":["GB","US"],"is_corresponding":false,"raw_author_name":"Yuval Peres","raw_affiliation_strings":["peres@microsoft.com"],"affiliations":[{"raw_affiliation_string":"peres@microsoft.com","institution_ids":["https://openalex.org/I4210164937","https://openalex.org/I1290206253"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065857248"],"corresponding_institution_ids":["https://openalex.org/I181233156"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.00298211,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"117","issue":"3","first_page":"220","last_page":"220"},"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":0.9940000176429749,"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":0.9940000176429749,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9934999942779541,"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":0.9672999978065491,"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/ergodic-theory","display_name":"Ergodic theory","score":0.7082890272140503},{"id":"https://openalex.org/keywords/hebrew","display_name":"Hebrew","score":0.5772549510002136},{"id":"https://openalex.org/keywords/center","display_name":"Center (category theory)","score":0.5516850352287292},{"id":"https://openalex.org/keywords/principal","display_name":"Principal (computer security)","score":0.5035461783409119},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4957831799983978},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.48080745339393616},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.4526141285896301},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.4409516155719757},{"id":"https://openalex.org/keywords/probability-theory","display_name":"Probability theory","score":0.41890794038772583},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3947772979736328},{"id":"https://openalex.org/keywords/sociology","display_name":"Sociology","score":0.3377910256385803},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23327761888504028},{"id":"https://openalex.org/keywords/history","display_name":"History","score":0.19040924310684204},{"id":"https://openalex.org/keywords/classics","display_name":"Classics","score":0.17391222715377808},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13882964849472046},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13569936156272888},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1345289945602417}],"concepts":[{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.7082890272140503},{"id":"https://openalex.org/C91304198","wikidata":"https://www.wikidata.org/wiki/Q9288","display_name":"Hebrew","level":2,"score":0.5772549510002136},{"id":"https://openalex.org/C2779463800","wikidata":"https://www.wikidata.org/wiki/Q5062222","display_name":"Center (category theory)","level":2,"score":0.5516850352287292},{"id":"https://openalex.org/C144559511","wikidata":"https://www.wikidata.org/wiki/Q2986279","display_name":"Principal (computer security)","level":2,"score":0.5035461783409119},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4957831799983978},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.48080745339393616},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.4526141285896301},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.4409516155719757},{"id":"https://openalex.org/C122203268","wikidata":"https://www.wikidata.org/wiki/Q5862903","display_name":"Probability theory","level":2,"score":0.41890794038772583},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3947772979736328},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.3377910256385803},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23327761888504028},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.19040924310684204},{"id":"https://openalex.org/C74916050","wikidata":"https://www.wikidata.org/wiki/Q841090","display_name":"Classics","level":1,"score":0.17391222715377808},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13882964849472046},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13569936156272888},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1345289945602417},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4169/000298910x480072","is_oa":false,"landing_page_url":"https://doi.org/10.4169/000298910x480072","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W637496756","https://openalex.org/W1532790179","https://openalex.org/W1600293573","https://openalex.org/W1965207838","https://openalex.org/W1974824584","https://openalex.org/W1987794091","https://openalex.org/W2034537320","https://openalex.org/W2070165567","https://openalex.org/W2076920623","https://openalex.org/W2130050451","https://openalex.org/W2139501386","https://openalex.org/W2145037371","https://openalex.org/W2167064216","https://openalex.org/W2254492281","https://openalex.org/W2332078328","https://openalex.org/W2579714562","https://openalex.org/W3015706207","https://openalex.org/W4291439952"],"related_works":["https://openalex.org/W2390585021","https://openalex.org/W50969306","https://openalex.org/W412641959","https://openalex.org/W1976009970","https://openalex.org/W2044004505","https://openalex.org/W2779828239","https://openalex.org/W2341040961","https://openalex.org/W3154976382","https://openalex.org/W4292101436","https://openalex.org/W2259764508"],"abstract_inverted_index":{"Click":[0],"to":[1,5],"increase":[2],"image":[3,7],"sizeClick":[4],"decrease":[6],"size":[8],"Additional":[9],"informationNotes":[10],"on":[11],"contributorsDavid":[12],"A.":[13,15],"LevinDAVID":[14],"LEVIN":[16],"(Ph.D.":[17,57],"University":[18,31,85,92],"of":[19,27,32,46,68,86,93,100,108,123,130,156,164],"California,":[20,87],"Berkeley,":[21],"1999)":[22],"is":[23,43,62,78,97],"an":[24,80,148],"assistant":[25],"professor":[26,82],"mathematics":[28],"at":[29,72,83,90,151],"the":[30,47,69,84,91,98,109,140,152,160],"Oregon.":[33],"His":[34,117],"research":[35,104,118],"interests":[36,119],"are":[37],"in":[38,75],"probability":[39,124],"theory,":[40,125,132,134],"and":[41,50,66,89,106,112,135,143,146,159],"he":[42],"a":[44,63],"co-author":[45,107],"bookMarkov":[48,110],"Chains":[49,111],"Mixing":[51,113],"Times":[52,114],"(AMS,":[53,115],"2008).Yuval":[54],"PeresYUVAL":[55],"PERES":[56],"Hebrew":[58],"University,":[59],"Jerusalem,":[60],"1990)":[61],"principal":[64],"researcher":[65],"manager":[67],"Theory":[70],"Group":[71],"Microsoft":[73],"Research":[74],"Redmond.":[76],"He":[77,96,138],"also":[79],"adjunct":[81],"Berkeley":[88],"Washington,":[94],"Seattle.":[95],"author":[99],"more":[101],"than":[102],"150":[103],"papers":[105],"2008).":[116],"include":[120],"most":[121],"areas":[122],"as":[126,128],"well":[127],"parts":[129],"ergodic":[131],"game":[133],"information":[136],"theory.":[137],"received":[139],"Rollo":[141],"Davidson":[142],"Loeve":[144],"prizes,":[145],"was":[147],"invited":[149],"speaker":[150],"2002":[153],"International":[154],"Congress":[155,163],"Mathematics":[157,165],"(Beijing)":[158],"2008":[161],"European":[162],"(Amsterdam).":[166]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}