{"id":"https://openalex.org/W7220934550","doi":"https://doi.org/10.48550/arxiv.2610.09949","title":"Ergodic measures of intermediate entropies for amenable group actions with an approximate product property","display_name":"Ergodic measures of intermediate entropies for amenable group actions with an approximate product property","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220934550","doi":"https://doi.org/10.48550/arxiv.2610.09949"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.09949","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09949","pdf_url":"https://arxiv.org/pdf/2610.09949","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.09949","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157987875","display_name":"Wenda Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I158842170","display_name":"Chongqing University","ror":"https://ror.org/023rhb549","country_code":"CN","type":"education","lineage":["https://openalex.org/I158842170"]},{"id":"https://openalex.org/I63371133","display_name":"Chongqing Jiaotong University","ror":"https://ror.org/01t001k65","country_code":"CN","type":"education","lineage":["https://openalex.org/I63371133"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Wenda","raw_affiliation_strings":["College of Mathematics and Statistic , Chongqing University , Chongqing 401331 , China","College of Mathematics and Statistics , Chongqing Jiaotong University , Chongqing 400074 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistic , Chongqing University , Chongqing 401331 , China","institution_ids":["https://openalex.org/I158842170"]},{"raw_affiliation_string":"College of Mathematics and Statistics , Chongqing Jiaotong University , Chongqing 400074 , China","institution_ids":["https://openalex.org/I63371133"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5157929900","display_name":"Xiankun Ren","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I63371133","display_name":"Chongqing Jiaotong University","ror":"https://ror.org/01t001k65","country_code":"CN","type":"education","lineage":["https://openalex.org/I63371133"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ren, Xiankun","raw_affiliation_strings":["College of Mathematics and Statistics , Chongqing Jiaotong University , Chongqing 400074 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics , Chongqing Jiaotong University , Chongqing 400074 , China","institution_ids":["https://openalex.org/I63371133"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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":0.9980000257492065,"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":0.9980000257492065,"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":0.000699999975040555,"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"}},{"id":"https://openalex.org/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":9.999999747378752e-05,"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/amenable-group-actions","display_name":"amenable group actions","score":0.8199999928474426},{"id":"https://openalex.org/keywords/ergodic-measures","display_name":"ergodic measures","score":0.8040000200271606},{"id":"https://openalex.org/keywords/continuous-group-actions","display_name":"continuous group actions","score":0.5659999847412109}],"concepts":[{"id":"https://openalex.org/C58179670","wikidata":"https://www.wikidata.org/wiki/Q1857002","display_name":"Amenable group","level":3,"score":0.82669997215271},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7979000210762024},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.7286999821662903},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.660099983215332},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.5625},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.538100004196167},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.5063999891281128},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4878000020980835},{"id":"https://openalex.org/C138673069","wikidata":"https://www.wikidata.org/wiki/Q322229","display_name":"Tracing","level":2,"score":0.4828000068664551},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4291999936103821},{"id":"https://openalex.org/C131715654","wikidata":"https://www.wikidata.org/wiki/Q288465","display_name":"Group action","level":3,"score":0.41990000009536743},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4027000069618225},{"id":"https://openalex.org/C2776379255","wikidata":"https://www.wikidata.org/wiki/Q3406705","display_name":"Crossed product","level":3,"score":0.4009000062942505},{"id":"https://openalex.org/C75066664","wikidata":"https://www.wikidata.org/wiki/Q291126","display_name":"Semidirect product","level":3,"score":0.3720000088214874},{"id":"https://openalex.org/C162362422","wikidata":"https://www.wikidata.org/wiki/Q1363919","display_name":"Second-countable space","level":3,"score":0.3582000136375427},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.352400004863739},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.31540000438690186},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.298799991607666},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.29580000042915344},{"id":"https://openalex.org/C201779956","wikidata":"https://www.wikidata.org/wiki/Q5426803","display_name":"Ergodicity","level":2,"score":0.2840999960899353},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.2833000123500824},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28049999475479126},{"id":"https://openalex.org/C87945829","wikidata":"https://www.wikidata.org/wiki/Q1353233","display_name":"Conjugacy class","level":2,"score":0.2538999915122986},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.09949","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09949","pdf_url":"https://arxiv.org/pdf/2610.09949","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"doi:10.48550/arxiv.2610.09949","doi":"https://doi.org/10.48550/arxiv.2610.09949","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.09949","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.09949","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.09949","pdf_url":"https://arxiv.org/pdf/2610.09949","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G6892761941","display_name":null,"funder_award_id":"CSTB2025NSCQ","funder_id":"https://openalex.org/F4320323172","funder_display_name":"Natural Science Foundation of Chongqing"},{"id":"https://openalex.org/G8896436568","display_name":null,"funder_award_id":"2025CDJZKPT-09","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320323172","display_name":"Natural Science Foundation of Chongqing","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220934550.pdf","grobid_xml":"https://content.openalex.org/works/W7220934550.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7162019876","https://openalex.org/W7202279559"],"related_works":["https://openalex.org/W2282690754","https://openalex.org/W4405178837","https://openalex.org/W2963556326","https://openalex.org/W2080759084","https://openalex.org/W2809616239","https://openalex.org/W7095469389","https://openalex.org/W7163383031","https://openalex.org/W2067791818","https://openalex.org/W3094491515","https://openalex.org/W3170507004"],"abstract_inverted_index":{"We":[0,12,38],"study":[1],"entropy":[2,70],"realization":[3],"for":[4,18,62],"continuous":[5],"actions":[6,21],"of":[7,27,48,65],"infinite":[8],"countable":[9],"amenable":[10,19],"groups.":[11],"introduce":[13],"an":[14],"approximate":[15],"product":[16],"property":[17,42],"group":[20],"that":[22,40],"permits":[23],"a":[24,59],"small":[25],"proportion":[26],"tracing":[28,66],"mistakes":[29],"on":[30],"prescribed":[31],"pairwise":[32],"disjoint,":[33],"sufficiently":[34],"invariant":[35,50],"finite":[36],"sets.":[37],"prove":[39],"this":[41],"implies":[43],"entropy-denseness":[44],"and":[45],"almost":[46,72],"entropy-approximability":[47,73],"every":[49,78],"measure.":[51],"The":[52],"construction":[53],"combines":[54],"zero-entropy":[55],"exact":[56],"tilings":[57],"with":[58],"finite-block":[60],"estimate":[61],"the":[63],"complexity":[64],"mistakes.":[67],"Under":[68],"asymptotic":[69],"expansiveness,":[71],"upgrades":[74],"to":[75],"entropy-approximability.":[76],"For":[77],"$0\\leq\u03b1":[79]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}