{"id":"https://openalex.org/W2996843894","doi":null,"title":"Statistical Invariance of Betti Numbers in the Thermodynamic Regime","display_name":"Statistical Invariance of Betti Numbers in the Thermodynamic Regime","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W2996843894","mag":"2996843894"},"language":"en","primary_location":{"id":"mag:2996843894","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2001.00220.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2001.00220.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074260201","display_name":"Siddharth Vishwanath","orcid":"https://orcid.org/0000-0002-2870-6465","observed_orcids":["https://orcid.org/0000-0002-2870-6465"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Siddharth Vishwanath","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012922872","display_name":"Kenji Fukumizu","orcid":"https://orcid.org/0000-0002-3488-2625","observed_orcids":["https://orcid.org/0000-0002-3488-2625"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kenji Fukumizu","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-3488-2625","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112602962","display_name":"Satoshi Kuriki","orcid":"https://orcid.org/0009-0000-1509-9013","observed_orcids":["https://orcid.org/0009-0000-1509-9013"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Satoshi Kuriki","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0000-1509-9013","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109582233","display_name":"Bharath K. Sriperumbudur","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bharath K. Sriperumbudur","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":null,"has_fulltext":false,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.0,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/betti-numbers","display_name":"Betti numbers","score":0.9760000109672546},{"id":"https://openalex.org/keywords/topological-inference","display_name":"topological inference","score":0.8320000171661377},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"topological data analysis","score":0.8999999761581421},{"id":"https://openalex.org/keywords/parametric-inference","display_name":"parametric inference","score":0.8629999756813049},{"id":"https://openalex.org/keywords/statistical-invariance","display_name":"statistical invariance","score":0.8460000157356262},{"id":"https://openalex.org/keywords/asymptotic-behavior","display_name":"asymptotic behavior","score":0.7919999957084656},{"id":"https://openalex.org/keywords/simplicial-complex","display_name":"simplicial complexes","score":0.7940000295639038},{"id":"https://openalex.org/keywords/high-dimensional-data","display_name":"high-dimensional data","score":0.5139999985694885}],"concepts":[{"id":"https://openalex.org/C129621563","wikidata":"https://www.wikidata.org/wiki/Q429593","display_name":"Betti number","level":2,"score":0.6904861330986023},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.6039726734161377},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.5569517016410828},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.5505252480506897},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5481253266334534},{"id":"https://openalex.org/C2776477805","wikidata":"https://www.wikidata.org/wiki/Q4460773","display_name":"Topological data analysis","level":2,"score":0.5138445496559143},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.49651676416397095},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4501101076602936},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.41612616181373596},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34511756896972656},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.17549309134483337},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16755038499832153},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1470431089401245},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13820722699165344},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09442475438117981}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2996843894","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2001.00220.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2996843894","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2001.00220.pdf","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W33547082","https://openalex.org/W152787284","https://openalex.org/W749223900","https://openalex.org/W1031083702","https://openalex.org/W1492288577","https://openalex.org/W1523421742","https://openalex.org/W1595105216","https://openalex.org/W1596721197","https://openalex.org/W1600738178","https://openalex.org/W1859601646","https://openalex.org/W1965432148","https://openalex.org/W1986280275","https://openalex.org/W2002411913","https://openalex.org/W2037613900","https://openalex.org/W2037817770","https://openalex.org/W2065833332","https://openalex.org/W2091574535","https://openalex.org/W2096736341","https://openalex.org/W2099973661","https://openalex.org/W2120672285","https://openalex.org/W2124331852","https://openalex.org/W2135610119","https://openalex.org/W2144044408","https://openalex.org/W2261714614","https://openalex.org/W2272927094","https://openalex.org/W2509446124","https://openalex.org/W2563576120","https://openalex.org/W2611241299","https://openalex.org/W2855166621","https://openalex.org/W2898403988","https://openalex.org/W2903033611","https://openalex.org/W2962816428","https://openalex.org/W2962914982","https://openalex.org/W2963154349","https://openalex.org/W2969351507","https://openalex.org/W3013843370","https://openalex.org/W3023779798","https://openalex.org/W3040586665","https://openalex.org/W3043283455","https://openalex.org/W3140579943","https://openalex.org/W4233907720"],"related_works":["https://openalex.org/W4401643512","https://openalex.org/W2123979496","https://openalex.org/W4410113350","https://openalex.org/W2402584820","https://openalex.org/W2767698434","https://openalex.org/W2183649102","https://openalex.org/W2883081389","https://openalex.org/W2495708099","https://openalex.org/W3088291654","https://openalex.org/W2963653254"],"abstract_inverted_index":{"Topological":[0],"Data":[1],"Analysis":[2],"(TDA)":[3],"has":[4,27],"become":[5],"a":[6,61,68,84],"promising":[7],"tool":[8],"to":[9],"uncover":[10],"low-dimensional":[11],"features":[12],"from":[13,83],"high-dimensional":[14],"data.":[15],"Notwithstanding":[16],"the":[17,38,44,91,96,103,109],"advantages":[18],"afforded":[19],"by":[20,30,67],"TDA,":[21],"its":[22],"adoption":[23],"in":[24,50,125],"statistical":[25],"methodology":[26],"been":[28],"limited":[29],"several":[31],"reasons.":[32],"In":[33],"this":[34,126],"paper":[35],"we":[36],"study":[37],"framework":[39],"of":[40,46,64,90,99,111],"topological":[41,104,121],"inference":[42,49,122],"through":[43],"lens":[45],"classical":[47],"parametric":[48,62,106,127],"statistics.":[51],"Suppose":[52],"$\\mathcal{P}":[53],"=":[54,73],"\\{\\mathbb{P}_\\theta":[55],":":[56],"\\theta":[57],"\\in":[58],"\\Theta\\}$":[59],"is":[60,78,123],"family":[63],"distributions":[65],"indexed":[66],"set":[69],"$\\Theta$,":[70],"and":[71,105,116],"$\\mathbb{X}_n":[72],"\\{\\mathbf{X}_1,":[74],"\\mathbf{X}_2,":[75],"\\dots,":[76],"\\mathbf{X}_n\\}$":[77],"observed":[79],"iid":[80],"at":[81],"random":[82],"distribution":[85,110],"$\\mathbb{P}_\\theta$.":[86],"The":[87],"asymptotic":[88],"behaviour":[89],"Betti":[92],"numbers":[93],"associated":[94],"with":[95],"Cech":[97],"complex":[98],"$\\mathbb{X}_n$":[100],"contain":[101],"both":[102],"information":[107],"about":[108],"points.":[112],"We":[113],"investigate":[114],"necessary":[115],"sufficient":[117],"conditions":[118],"under":[119],"which":[120],"possible":[124],"setup.":[128]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2020-01-10T00:00:00"}
