{"id":"https://openalex.org/W2107927170","doi":"https://doi.org/10.1017/s0963548314000364","title":"P\u00f3lya Urns Via the Contraction Method","display_name":"P\u00f3lya Urns Via the Contraction Method","publication_year":2014,"publication_date":"2014-09-01","ids":{"openalex":"https://openalex.org/W2107927170","doi":"https://doi.org/10.1017/s0963548314000364","mag":"2107927170"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548314000364","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548314000364","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1301.3404","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010569018","display_name":"Margarete Knape","orcid":null},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"MARGARETE KNAPE","raw_affiliation_strings":["Institute for Mathematics, J. W. Goethe University, 60054 Frankfurt a.M., Germany (e-mail:"],"affiliations":[{"raw_affiliation_string":"Institute for Mathematics, J. W. Goethe University, 60054 Frankfurt a.M., Germany (e-mail:","institution_ids":["https://openalex.org/I114090438"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056428246","display_name":"Ralph Neininger","orcid":"https://orcid.org/0000-0003-3975-1293"},"institutions":[{"id":"https://openalex.org/I114090438","display_name":"Goethe University Frankfurt","ror":"https://ror.org/04cvxnb49","country_code":"DE","type":"education","lineage":["https://openalex.org/I114090438"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"RALPH NEININGER","raw_affiliation_strings":["Institute for Mathematics, J. W. Goethe University, 60054 Frankfurt a.M., Germany (e-mail:"],"affiliations":[{"raw_affiliation_string":"Institute for Mathematics, J. W. Goethe University, 60054 Frankfurt a.M., Germany (e-mail:","institution_ids":["https://openalex.org/I114090438"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010569018"],"corresponding_institution_ids":["https://openalex.org/I114090438"],"apc_list":null,"apc_paid":null,"fwci":7.5395,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.98345312,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"23","issue":"6","first_page":"1148","last_page":"1186"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.998199999332428,"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":0.998199999332428,"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":0.9941999912261963,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9833999872207642,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7582420110702515},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.7465637922286987},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.655224621295929},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.5467596650123596},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.511328399181366},{"id":"https://openalex.org/keywords/limit-of-a-function","display_name":"Limit of a function","score":0.5074195265769958},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.41396963596343994},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3912024199962616},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1144024133682251},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10532781481742859}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7582420110702515},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.7465637922286987},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.655224621295929},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.5467596650123596},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.511328399181366},{"id":"https://openalex.org/C19448537","wikidata":"https://www.wikidata.org/wiki/Q33540","display_name":"Limit of a function","level":3,"score":0.5074195265769958},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.41396963596343994},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3912024199962616},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1144024133682251},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10532781481742859},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1017/s0963548314000364","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548314000364","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1301.3404","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1301.3404","pdf_url":"https://arxiv.org/pdf/1301.3404","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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:CiteSeerX.psu:10.1.1.303.5056","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.303.5056","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uni-frankfurt.de/%7Eneiningr/polya_cont.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.433.1428","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.433.1428","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uni-frankfurt.de/~neiningr/polya_cont.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.765.2827","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.765.2827","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1301.3404.pdf","raw_type":"text"},{"id":"pmh:oai:publikationen.ub.uni-frankfurt.de:32284","is_oa":false,"landing_page_url":"http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32284","pdf_url":null,"source":{"id":"https://openalex.org/S4306400432","display_name":"Publication Server of Goethe University Frankfurt am Main (Goethe University Frankfurt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114090438","host_organization_name":"Goethe University Frankfurt","host_organization_lineage":["https://openalex.org/I114090438"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"doctoralthesis"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1301.3404","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1301.3404","pdf_url":"https://arxiv.org/pdf/1301.3404","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[{"score":0.5099999904632568,"display_name":"Life in Land","id":"https://metadata.un.org/sdg/15"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W1511251174","https://openalex.org/W1511269633","https://openalex.org/W1573314657","https://openalex.org/W1608334810","https://openalex.org/W1611936726","https://openalex.org/W1964327778","https://openalex.org/W1964588325","https://openalex.org/W1968457938","https://openalex.org/W1974315986","https://openalex.org/W1984899798","https://openalex.org/W1987624250","https://openalex.org/W1990085540","https://openalex.org/W2002682396","https://openalex.org/W2014712015","https://openalex.org/W2024811208","https://openalex.org/W2038681797","https://openalex.org/W2042464140","https://openalex.org/W2054616111","https://openalex.org/W2064294696","https://openalex.org/W2067707835","https://openalex.org/W2087183702","https://openalex.org/W2088195732","https://openalex.org/W2091386360","https://openalex.org/W2092872439","https://openalex.org/W2107927170","https://openalex.org/W2113913510","https://openalex.org/W2119121146","https://openalex.org/W2142568813","https://openalex.org/W2143041542","https://openalex.org/W2144905577","https://openalex.org/W2149223272","https://openalex.org/W2150895539","https://openalex.org/W2155841350","https://openalex.org/W2167624711","https://openalex.org/W2348112403","https://openalex.org/W2567327503","https://openalex.org/W2592489754","https://openalex.org/W2797066131","https://openalex.org/W2951034931","https://openalex.org/W2951421176","https://openalex.org/W2951629938","https://openalex.org/W2962679402","https://openalex.org/W3015706207","https://openalex.org/W3038019923","https://openalex.org/W3100572514","https://openalex.org/W3100757862","https://openalex.org/W4232020064","https://openalex.org/W4255565618","https://openalex.org/W4256358797","https://openalex.org/W4300324570","https://openalex.org/W6642594851","https://openalex.org/W6681057447","https://openalex.org/W6731558416"],"related_works":["https://openalex.org/W2348480070","https://openalex.org/W4385379825","https://openalex.org/W4224286489","https://openalex.org/W1564609195","https://openalex.org/W2390957572","https://openalex.org/W2381670468","https://openalex.org/W3000711322","https://openalex.org/W2367503346","https://openalex.org/W2355429547","https://openalex.org/W2370289464"],"abstract_inverted_index":{"We":[0,77],"propose":[1],"an":[2],"approach":[3,80],"to":[4,42,68,81,90],"analysing":[5],"the":[6,14,25,28,51,54,63],"asymptotic":[7,103],"behaviour":[8],"of":[9,24,27,38,45,53,56,58,72,84],"P\u00f3lya":[10,86],"urns":[11,87],"based":[12],"on":[13],"contraction":[15,64],"method.":[16],"For":[17],"this,":[18],"a":[19,43,82],"new":[20],"combinatorial":[21],"discrete-time":[22],"embedding":[23],"evolution":[26],"urn":[29],"into":[30],"random":[31],"rooted":[32],"trees":[33,40],"is":[34],"developed.":[35],"A":[36],"decomposition":[37],"these":[39],"leads":[41],"system":[44],"recursive":[46,73],"distributional":[47,74,105],"equations":[48,75],"which":[49],"capture":[50],"distributions":[52,100],"numbers":[55],"balls":[57],"each":[59],"colour.":[60],"Ideas":[61],"from":[62],"method":[65],"are":[66],"used":[67],"study":[69],"such":[70],"systems":[71],"asymptotically.":[76],"apply":[78],"our":[79],"couple":[83],"concrete":[85],"that":[88],"lead":[89],"limit":[91,95,99],"laws":[92],"with":[93,97,102],"normal":[94],"distributions,":[96],"non-normal":[98],"and":[101],"periodic":[104],"behaviour.":[106]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}