{"id":"https://openalex.org/W7130571663","doi":"https://doi.org/10.1137/s0040585x97t99263x","title":"On Cocycles over Ergodic Transformations and Barycenters","display_name":"On Cocycles over Ergodic Transformations and Barycenters","publication_year":2026,"publication_date":"2026-02-01","ids":{"openalex":"https://openalex.org/W7130571663","doi":"https://doi.org/10.1137/s0040585x97t99263x"},"language":"en","primary_location":{"id":"doi:10.1137/s0040585x97t99263x","doi":"https://doi.org/10.1137/s0040585x97t99263x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0040585x97t99263x","pdf_url":null,"source":{"id":"https://openalex.org/S177771411","display_name":"Theory of Probability and Its Applications","issn_l":"0040-585X","issn":["0040-585X","1095-7219"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Probability &amp; Its Applications","raw_type":"journal-article"},"volume":null,"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/A5077844095","display_name":"M. E. Lipatov","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"M. E. Lipatov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5077844095"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.28727643,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":"4","first_page":"593","last_page":"601"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9833999872207642,"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":0.9833999872207642,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.0034000000450760126,"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":0.0017999999690800905,"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/cocycles","display_name":"cocycles","score":0.7429999709129333},{"id":"https://openalex.org/keywords/ergodic-transformations","display_name":"ergodic transformations","score":0.949999988079071},{"id":"https://openalex.org/keywords/barycenter","display_name":"barycenter","score":0.9539999961853027},{"id":"https://openalex.org/keywords/symmetric-spaces","display_name":"symmetric spaces","score":0.7310000061988831},{"id":"https://openalex.org/keywords/recurrence","display_name":"recurrence","score":0.9909999966621399}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9182999730110168},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.8952999711036682},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5910999774932861},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5830000042915344},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.5784000158309937},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.5041999816894531},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.3068999946117401},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.29899999499320984},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28949999809265137},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.2741999924182892}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0040585x97t99263x","doi":"https://doi.org/10.1137/s0040585x97t99263x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0040585x97t99263x","pdf_url":null,"source":{"id":"https://openalex.org/S177771411","display_name":"Theory of Probability and Its Applications","issn_l":"0040-585X","issn":["0040-585X","1095-7219"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-scientific","cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Probability &amp; Its Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W156547846","https://openalex.org/W1565171775","https://openalex.org/W1809786681","https://openalex.org/W1986372238","https://openalex.org/W1989597429","https://openalex.org/W2020248993","https://openalex.org/W2063263217","https://openalex.org/W2065516294","https://openalex.org/W2079175624","https://openalex.org/W2094532370","https://openalex.org/W2134086356","https://openalex.org/W2603853566","https://openalex.org/W4220757000"],"related_works":[],"abstract_inverted_index":{"The":[0],"barycenters":[1],"of":[2,6,13,24,28,33],"measures":[3],"on":[4,37],"boundaries":[5],"symmetric":[7],"spaces":[8],"are":[9],"applied":[10],"for":[11],"classification":[12],"linear":[14],"cocycles":[15],"over":[16],"ergodic":[17],"transformations.":[18],"We":[19],"also":[20],"consider":[21],"the":[22],"case":[23],"semisimple":[25],"Lie":[26],"groups":[27],"rank":[29],"$1$":[30],"and":[31],"recurrence":[32],"stationary":[34],"random":[35],"walks":[36],"them.":[38]},"counts_by_year":[],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2026-02-20T00:00:00"}
