{"id":"https://openalex.org/W2095343591","doi":"https://doi.org/10.1142/s0218196715400081","title":"Markov chains, ${\\mathscr R}$-trivial monoids and representation theory","display_name":"Markov chains, ${\\mathscr R}$-trivial monoids and representation theory","publication_year":2015,"publication_date":"2015-01-09","ids":{"openalex":"https://openalex.org/W2095343591","doi":"https://doi.org/10.1142/s0218196715400081","mag":"2095343591"},"language":"en","primary_location":{"id":"doi:10.1142/s0218196715400081","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196715400081","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1401.4250","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Arvind Ayyer","orcid":null},"institutions":[{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Arvind Ayyer","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Science, Bangalore - 560012, India","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Anne Schilling","orcid":null},"institutions":[{"id":"https://openalex.org/I84218800","display_name":"University of California, Davis","ror":"https://ror.org/05rrcem69","country_code":"US","type":"education","lineage":["https://openalex.org/I84218800"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anne Schilling","raw_affiliation_strings":["Department of Mathematics, University of California Davis, One Shields Ave., Davis, California 95616-8633, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California Davis, One Shields Ave., Davis, California 95616-8633, USA","institution_ids":["https://openalex.org/I84218800"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Benjamin Steinberg","orcid":null},"institutions":[{"id":"https://openalex.org/I125687163","display_name":"City College of New York","ror":"https://ror.org/00wmhkr98","country_code":"US","type":"education","lineage":["https://openalex.org/I125687163"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Benjamin Steinberg","raw_affiliation_strings":["Department of Mathematics, City College of New York, Convent Avenue at 138th Street, New York, 10031, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City College of New York, Convent Avenue at 138th Street, New York, 10031, USA","institution_ids":["https://openalex.org/I125687163"]}]},{"author_position":"last","author":{"id":null,"display_name":"Nicolas M. Thi\u00e9ry","orcid":null},"institutions":[{"id":"https://openalex.org/I102197404","display_name":"Universit\u00e9 Paris-Sud","ror":"https://ror.org/028rypz17","country_code":"FR","type":"education","lineage":["https://openalex.org/I102197404"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nicolas M. Thi\u00e9ry","raw_affiliation_strings":["CNRS, Orsay, F-91405, France","Laboratoire de Recherche en Informatique, Universit\u00e9 Paris-Sud, Orsay, F-91405, France"],"affiliations":[{"raw_affiliation_string":"CNRS, Orsay, F-91405, France","institution_ids":["https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Laboratoire de Recherche en Informatique, Universit\u00e9 Paris-Sud, Orsay, F-91405, France","institution_ids":["https://openalex.org/I102197404"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I59270414"],"apc_list":null,"apc_paid":null,"fwci":8.8881,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.98545918,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"25","issue":"01n02","first_page":"169","last_page":"231"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.4244000017642975,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.4244000017642975,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.14100000262260437,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.1177000030875206,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/markov-chain","display_name":"Markov chain","score":0.7350999712944031},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.6288999915122986},{"id":"https://openalex.org/keywords/stochastic-matrix","display_name":"Stochastic matrix","score":0.460099995136261},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.44839999079704285},{"id":"https://openalex.org/keywords/mixing","display_name":"Mixing (physics)","score":0.43149998784065247},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.4124999940395355},{"id":"https://openalex.org/keywords/monoid","display_name":"Monoid","score":0.4059999883174896},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.40059998631477356},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.37470000982284546}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8999000191688538},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7350999712944031},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.6288999915122986},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4641999900341034},{"id":"https://openalex.org/C49555168","wikidata":"https://www.wikidata.org/wiki/Q176583","display_name":"Stochastic matrix","level":3,"score":0.460099995136261},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.44839999079704285},{"id":"https://openalex.org/C138777275","wikidata":"https://www.wikidata.org/wiki/Q6884054","display_name":"Mixing (physics)","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41339999437332153},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.4124999940395355},{"id":"https://openalex.org/C206901836","wikidata":"https://www.wikidata.org/wiki/Q208237","display_name":"Monoid","level":2,"score":0.4059999883174896},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.40059998631477356},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.37470000982284546},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3637999892234802},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3603000044822693},{"id":"https://openalex.org/C197273675","wikidata":"https://www.wikidata.org/wiki/Q13220368","display_name":"Representation theory","level":2,"score":0.3118000030517578},{"id":"https://openalex.org/C76408418","wikidata":"https://www.wikidata.org/wiki/Q5419314","display_name":"Examples of Markov chains","level":5,"score":0.3089999854564667},{"id":"https://openalex.org/C106666656","wikidata":"https://www.wikidata.org/wiki/Q6771323","display_name":"Markov kernel","level":5,"score":0.2996000051498413},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.28540000319480896},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.2847000062465668},{"id":"https://openalex.org/C189973286","wikidata":"https://www.wikidata.org/wiki/Q176695","display_name":"Markov property","level":4,"score":0.27390000224113464},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.27390000224113464},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.2703000009059906},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.2671000063419342},{"id":"https://openalex.org/C97074811","wikidata":"https://www.wikidata.org/wiki/Q6771322","display_name":"Markov chain mixing time","level":5,"score":0.2572999894618988},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.25049999356269836}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0218196715400081","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218196715400081","pdf_url":null,"source":{"id":"https://openalex.org/S23260266","display_name":"International Journal of Algebra and Computation","issn_l":"0218-1967","issn":["0218-1967","1793-6500"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Algebra and Computation","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1401.4250","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.4250","pdf_url":"https://arxiv.org/pdf/1401.4250","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:HAL:hal-01121178v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01121178","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":"International Journal of Algebra and Computation, 2015, pp.1540008. ⟨10.1142/s0218196715400081⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1401.4250","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.4250","pdf_url":"https://arxiv.org/pdf/1401.4250","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":65,"referenced_works":["https://openalex.org/W294334239","https://openalex.org/W637655573","https://openalex.org/W1487875360","https://openalex.org/W1498166880","https://openalex.org/W1518573520","https://openalex.org/W1586417893","https://openalex.org/W1598605567","https://openalex.org/W1828146001","https://openalex.org/W1856287640","https://openalex.org/W1964448862","https://openalex.org/W1966435519","https://openalex.org/W1968040597","https://openalex.org/W1970679756","https://openalex.org/W1974048717","https://openalex.org/W1976674167","https://openalex.org/W1987488577","https://openalex.org/W1988818775","https://openalex.org/W1989674800","https://openalex.org/W1993259034","https://openalex.org/W1995154714","https://openalex.org/W1998602421","https://openalex.org/W2004035289","https://openalex.org/W2004288336","https://openalex.org/W2005830269","https://openalex.org/W2018457441","https://openalex.org/W2020796024","https://openalex.org/W2023716289","https://openalex.org/W2035370987","https://openalex.org/W2037190943","https://openalex.org/W2037269616","https://openalex.org/W2037420999","https://openalex.org/W2042872239","https://openalex.org/W2044138171","https://openalex.org/W2050340036","https://openalex.org/W2051669952","https://openalex.org/W2054133346","https://openalex.org/W2056389572","https://openalex.org/W2057968941","https://openalex.org/W2073466607","https://openalex.org/W2075514521","https://openalex.org/W2076616949","https://openalex.org/W2079502209","https://openalex.org/W2080223186","https://openalex.org/W2089499170","https://openalex.org/W2095754162","https://openalex.org/W2107393965","https://openalex.org/W2124322517","https://openalex.org/W2125612913","https://openalex.org/W2133379784","https://openalex.org/W2134810677","https://openalex.org/W2143351557","https://openalex.org/W2166146452","https://openalex.org/W2284295789","https://openalex.org/W2315234012","https://openalex.org/W2318076643","https://openalex.org/W2737776333","https://openalex.org/W2997541814","https://openalex.org/W4205818646","https://openalex.org/W4206570602","https://openalex.org/W4212906638","https://openalex.org/W4233893779","https://openalex.org/W4238532454","https://openalex.org/W4253902644","https://openalex.org/W4302964898","https://openalex.org/W4403297261"],"related_works":[],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,39,41,111],"general":[3],"theory":[4],"of":[5,26,32,45,96,107,114],"Markov":[6,91],"chains":[7],"realizable":[8],"as":[9,64,74,76,84,102],"random":[10,103],"walks":[11,104],"on":[12,93,105],"[Formula:":[13],"see":[14],"text]-trivial":[15],"monoids.":[16],"It":[17],"provides":[18],"explicit":[19],"and":[20,49,88],"simple":[21],"formulas":[22],"for":[23,30,43,52,70],"the":[24,27,33,46,54,81,89],"eigenvalues":[25,34],"transition":[28,47],"matrix,":[29],"multiplicities":[31],"via":[35],"M\u00f6bius":[36],"inversion":[37],"along":[38],"lattice,":[40],"condition":[42],"diagonalizability":[44],"matrix":[48],"some":[50],"techniques":[51],"bounding":[53],"mixing":[55],"time.":[56],"In":[57],"addition,":[58],"we":[59,118],"discuss":[60],"several":[61],"examples,":[62],"such":[63,83],"Toom\u2013Tsetlin":[65],"models,":[66],"an":[67],"exchange":[68],"walk":[69],"finite":[71],"Coxeter":[72],"groups,":[73],"well":[75],"examples":[77,98],"previously":[78],"studied":[79],"by":[80],"authors,":[82],"nonabelian":[85],"sandpile":[86],"models":[87],"promotion":[90],"chain":[92],"posets.":[94],"Many":[95],"these":[97],"can":[99],"be":[100],"viewed":[101],"quotients":[106],"free":[108],"tree":[109],"monoids,":[110],"new":[112],"class":[113],"monoids":[115],"whose":[116],"combinatorics":[117],"develop.":[119]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}