{"id":"https://openalex.org/W197270207","doi":null,"title":"Matrix-valued random walks and variations on property AT","display_name":"Matrix-valued random walks and variations on property AT","publication_year":2008,"publication_date":"2008-11-30","ids":{"openalex":"https://openalex.org/W197270207","mag":"197270207"},"language":"en","primary_location":{"id":"pmh:oai:wwu.de:9317638a-ac3a-4fad-ab04-c58a0d2697b4","doi":null,"is_oa":true,"landing_page_url":"https://miami.uni-muenster.de/Record/9317638a-ac3a-4fad-ab04-c58a0d2697b4","pdf_url":"https://repositorium.uni-muenster.de/transfer/miami/9317638a-ac3a-4fad-ab04-c58a0d2697b4","source":{"id":"https://openalex.org/S4306402051","display_name":"URN:NBN Resolver for Germany & Switzerland (German National Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2802635041","host_organization_name":"Technische Informationsbibliothek (TIB)","host_organization_lineage":["https://openalex.org/I2802635041"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://repositorium.uni-muenster.de/transfer/miami/9317638a-ac3a-4fad-ab04-c58a0d2697b4","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078608927","display_name":"Thierry Giordano","orcid":"https://orcid.org/0000-0003-0758-1525","observed_orcids":["https://orcid.org/0000-0003-0758-1525"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Thierry Giordano","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5059414731","display_name":"David E. Handelman","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David H","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5141781623","display_name":"Communicated Joachim Cuntz","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Communicated Joachim Cuntz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7476,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.60311603,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9375,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9375,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.030799999833106995,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.008299999870359898,"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/dimension-groups","display_name":"dimension groups","score":0.8889999985694885},{"id":"https://openalex.org/keywords/ergodic-actions","display_name":"ergodic actions","score":0.7730000019073486},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.8270000219345093},{"id":"https://openalex.org/keywords/involutions","display_name":"involutions","score":0.7390000224113464},{"id":"https://openalex.org/keywords/free-group-actions","display_name":"free group actions","score":0.7839999794960022},{"id":"https://openalex.org/keywords/amenable-groups","display_name":"amenable groups","score":0.8410000205039978}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8256897926330566},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.7120220065116882},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6685025095939636},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.6356474757194519},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5933352708816528},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.5839753150939941},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.518198549747467},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4825660288333893},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4313514232635498},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.4226926565170288},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31528183817863464},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08130139112472534},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:wwu.de:9317638a-ac3a-4fad-ab04-c58a0d2697b4","doi":null,"is_oa":true,"landing_page_url":"https://miami.uni-muenster.de/Record/9317638a-ac3a-4fad-ab04-c58a0d2697b4","pdf_url":"https://repositorium.uni-muenster.de/transfer/miami/9317638a-ac3a-4fad-ab04-c58a0d2697b4","source":{"id":"https://openalex.org/S4306402051","display_name":"URN:NBN Resolver for Germany & Switzerland (German National Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2802635041","host_organization_name":"Technische Informationsbibliothek (TIB)","host_organization_lineage":["https://openalex.org/I2802635041"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.490.2403","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.490.2403","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://miami.uni-muenster.de/servlets/DerivateServlet/Derivate-4826/mjm_vol_1_03.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:wwu.de:9317638a-ac3a-4fad-ab04-c58a0d2697b4","doi":null,"is_oa":true,"landing_page_url":"https://miami.uni-muenster.de/Record/9317638a-ac3a-4fad-ab04-c58a0d2697b4","pdf_url":"https://repositorium.uni-muenster.de/transfer/miami/9317638a-ac3a-4fad-ab04-c58a0d2697b4","source":{"id":"https://openalex.org/S4306402051","display_name":"URN:NBN Resolver for Germany & Switzerland (German National Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2802635041","host_organization_name":"Technische Informationsbibliothek (TIB)","host_organization_lineage":["https://openalex.org/I2802635041"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W197270207.pdf","grobid_xml":"https://content.openalex.org/works/W197270207.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W159487936","https://openalex.org/W1490505438","https://openalex.org/W1517932056","https://openalex.org/W1544140021","https://openalex.org/W1592397385","https://openalex.org/W1966007443","https://openalex.org/W1970889539","https://openalex.org/W1983046429","https://openalex.org/W1997648816","https://openalex.org/W2000032061","https://openalex.org/W2001396077","https://openalex.org/W2023677036","https://openalex.org/W2045715539","https://openalex.org/W2056487814","https://openalex.org/W2057339196","https://openalex.org/W2094508941","https://openalex.org/W2096750502","https://openalex.org/W2119736295","https://openalex.org/W2155423371","https://openalex.org/W2164752578","https://openalex.org/W2326323046","https://openalex.org/W2328912295","https://openalex.org/W2562293972","https://openalex.org/W2798655805"],"related_works":["https://openalex.org/W2260796501","https://openalex.org/W2241216108","https://openalex.org/W4300834625","https://openalex.org/W7096553469","https://openalex.org/W1519391462","https://openalex.org/W2747347808","https://openalex.org/W2094103976","https://openalex.org/W2905918717","https://openalex.org/W2111493155","https://openalex.org/W1987012691"],"abstract_inverted_index":{"Abstract.":[0],"We":[1,65,171],"reformulate":[2],"matrix-valued":[3,96],"random":[4,97,136],"walks":[5,98],"and":[6,53,145,167],"their":[7],"associated":[8],"group":[9,182],"actions":[10,41,120,131,155],"in":[11,121],"terms":[12],"of":[13,29,51,71,86,103,109,142,179],"dimension":[14],"groups,":[15],"suitably":[16],"modified":[17],"to":[18,26,99,126],"deal":[19],"with":[20],"measure-theoretic":[21],"classifica-tion.":[22],"This":[23,47],"leads":[24],"naturally":[25],"a":[27,107,140,174,196,203],"notion":[28],"rank":[30,44],"denoted":[31],"AT(n),":[32],"for":[33,57,95,132],"integers":[34,73],"n":[35],"(approximately":[36],"transitive,":[37],"that":[38,77,148,159],"is,":[39],"AT,":[40,80],"constitute":[42],"the":[43,72,90,104,122,129,134,149,180],"one":[45],"situation).":[46],"yields":[48],"wide":[49],"classes":[50],"examples,":[52],"easily":[54],"verified":[55],"criteria":[56,94,105],"basic":[58],"properties":[59],"(such":[60],"as":[61,117],"ergodicity)":[62],"are":[63,115,124,169],"established.":[64],"present":[66,173],"an":[67,75,83,200,208],"(ergodic)":[68],"AT(2)":[69,188],"action":[70,178],"(from":[74],"involution)":[76],"is":[78,160,187,193],"not":[79,190],"effectively":[81],"answering":[82],"old":[84],"question":[85],"Thouvenot,":[87],"but":[88,192],"on":[89,111,152,183],"other":[91],"hand,":[92],"give":[93],"be":[100,127],"AT.":[101],"One":[102],"resembles":[106],"result":[108],"Mineka":[110],"mass":[112],"cancellation.":[113],"What":[114],"known":[116],"bounded":[118,153],"AT":[119,130,154,161,165],"literature":[123],"shown":[125],"exactly":[128],"which":[133,186],"corresponding":[135],"walk":[137],"comes":[138],"from":[139],"sequence":[141,198,205],"Poisson":[143],"distributions,":[144],"we":[146],"show":[147],"natural":[150],"involutions":[151],"have":[156],"orbit":[157],"space":[158],"(unlike":[162],"more":[163],"general":[164],"actions),":[166],"generically":[168],"bounded.":[170],"also":[172],"rather":[175],"unusual":[176],"ergodic":[177],"free":[181],"two":[184],"generators":[185],"(and":[189],"AT),":[191],"given":[194],"by":[195],"constant":[197,204],"(for":[199],"amenable":[201],"group,":[202],"would":[206],"yield":[207],"uninteresting":[209],"action).":[210],"I.":[211]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2025-10-10T00:00:00"}
