{"id":"https://openalex.org/W2963601914","doi":"https://doi.org/10.1002/rsa.20697","title":"On the vanishing of homology in random \u010cech complexes","display_name":"On the vanishing of homology in random \u010cech complexes","publication_year":2016,"publication_date":"2016-11-07","ids":{"openalex":"https://openalex.org/W2963601914","doi":"https://doi.org/10.1002/rsa.20697","mag":"2963601914"},"language":"en","primary_location":{"id":"doi:10.1002/rsa.20697","doi":"https://doi.org/10.1002/rsa.20697","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.20697","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-2","norway-2","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures &amp; Algorithms","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1507.06945","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5070671339","display_name":"Omer Bobrowski","orcid":"https://orcid.org/0000-0002-0860-7099","observed_orcids":["https://orcid.org/0000-0002-0860-7099"]},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Omer Bobrowski","raw_affiliation_strings":["Department of Electrical Engineering, Technion - Israel Institute of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Technion - Israel Institute of Technology","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073943501","display_name":"Shmuel Weinberger","orcid":"https://orcid.org/0000-0002-4315-9164","observed_orcids":["https://orcid.org/0000-0002-4315-9164"]},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shmuel Weinberger","raw_affiliation_strings":["Department of Mathematics, University of Chicago"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Chicago","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5070671339"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":{"value":4550,"currency":"USD","value_usd":4550},"apc_paid":null,"fwci":2.9173,"has_fulltext":true,"cited_by_count":35,"citation_normalized_percentile":{"value":0.9036006,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":98},"biblio":{"volume":"51","issue":"1","first_page":"14","last_page":"51"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9785000085830688,"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":0.9785000085830688,"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/T11830","display_name":"Point processes and geometric inequalities","score":0.012900000438094139,"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"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.0010000000474974513,"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/homology-groups","display_name":"homology groups","score":0.6449999809265137},{"id":"https://openalex.org/keywords/poisson-point-process","display_name":"Poisson point process","score":0.753000020980835},{"id":"https://openalex.org/keywords/torus","display_name":"torus","score":0.7850000262260437},{"id":"https://openalex.org/keywords/phase-transitions","display_name":"phase transitions","score":0.7940000295639038},{"id":"https://openalex.org/keywords/random-simplicial-complexes","display_name":"random simplicial complexes","score":0.777999997138977},{"id":"https://openalex.org/keywords/topological-data-analysis","display_name":"topological data analysis","score":0.7379999756813049}],"concepts":[{"id":"https://openalex.org/C9767117","wikidata":"https://www.wikidata.org/wiki/Q12510","display_name":"Torus","level":2,"score":0.7834147214889526},{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.7366445064544678},{"id":"https://openalex.org/C2776142590","wikidata":"https://www.wikidata.org/wiki/Q1164699","display_name":"struct","level":2,"score":0.6509287357330322},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.6060001254081726},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5682110786437988},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5360024571418762},{"id":"https://openalex.org/C139962677","wikidata":"https://www.wikidata.org/wiki/Q1095056","display_name":"Singular homology","level":3,"score":0.5344732403755188},{"id":"https://openalex.org/C2874115","wikidata":"https://www.wikidata.org/wiki/Q17099562","display_name":"Persistent homology","level":2,"score":0.524103045463562},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4891941547393799},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40877407789230347},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.30011624097824097},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.2846117615699768},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.21188944578170776},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.2066761553287506},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19848302006721497},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09034562110900879},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08314403891563416},{"id":"https://openalex.org/C515207424","wikidata":"https://www.wikidata.org/wiki/Q8066","display_name":"Amino acid","level":2,"score":0.06459665298461914},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05676901340484619},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1002/rsa.20697","doi":"https://doi.org/10.1002/rsa.20697","is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.20697","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-2","norway-2","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Random Structures &amp; Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1507.06945","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.06945","pdf_url":"https://arxiv.org/pdf/1507.06945","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":"mag:1914945357","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1507.06945.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},{"id":"doi:10.48550/arxiv.1507.06945","doi":"https://doi.org/10.48550/arxiv.1507.06945","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1507.06945","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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1507.06945","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1507.06945","pdf_url":"https://arxiv.org/pdf/1507.06945","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/G3053996755","display_name":"Problems in Geometric, Algebraic and Quantitative Topology","funder_award_id":"1510178","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4123259794","display_name":"Statistical and Applied Mathematical Sciences Institute","funder_award_id":"1127914","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5418073398","display_name":null,"funder_award_id":"FA9550\u201010\u20101\u20100436","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2963601914.pdf","grobid_xml":"https://content.openalex.org/works/W2963601914.grobid-xml"},"referenced_works_count":49,"referenced_works":["https://openalex.org/W33547082","https://openalex.org/W137677586","https://openalex.org/W630423399","https://openalex.org/W749223900","https://openalex.org/W1541118220","https://openalex.org/W1673212200","https://openalex.org/W1680861744","https://openalex.org/W1859601646","https://openalex.org/W1965334706","https://openalex.org/W1982869544","https://openalex.org/W1989181831","https://openalex.org/W1991566301","https://openalex.org/W2008318377","https://openalex.org/W2018582120","https://openalex.org/W2061678583","https://openalex.org/W2063776392","https://openalex.org/W2068871408","https://openalex.org/W2071391326","https://openalex.org/W2073443682","https://openalex.org/W2090464710","https://openalex.org/W2091574535","https://openalex.org/W2102346409","https://openalex.org/W2118268936","https://openalex.org/W2120672285","https://openalex.org/W2147123935","https://openalex.org/W2151087733","https://openalex.org/W2157071288","https://openalex.org/W2157878484","https://openalex.org/W2161491327","https://openalex.org/W2297068249","https://openalex.org/W2321124713","https://openalex.org/W2486762503","https://openalex.org/W2513044244","https://openalex.org/W2527487499","https://openalex.org/W2798062075","https://openalex.org/W2905110430","https://openalex.org/W2962885031","https://openalex.org/W2962914982","https://openalex.org/W2962934025","https://openalex.org/W2963121792","https://openalex.org/W2964131216","https://openalex.org/W2964154246","https://openalex.org/W3040586665","https://openalex.org/W3083418760","https://openalex.org/W4213199372","https://openalex.org/W4238406136","https://openalex.org/W4243631322","https://openalex.org/W4254707114","https://openalex.org/W4312512934"],"related_works":["https://openalex.org/W1914945357","https://openalex.org/W2964295082","https://openalex.org/W2950381279","https://openalex.org/W2609394492","https://openalex.org/W4206340959","https://openalex.org/W2120672285","https://openalex.org/W2785241152","https://openalex.org/W3024477531","https://openalex.org/W4297421245","https://openalex.org/W2343729008"],"abstract_inverted_index":{"We":[0],"compute":[1],"the":[2,14,32,38,49],"homology":[3,51,80],"of":[4,65],"random":[5],"\u010cech":[6,39],"complexes":[7],"over":[8],"a":[9,62,70],"homogeneous":[10],"Poisson":[11],"process":[12],"on":[13],"d-dimensional":[15],"torus,":[16],"and":[17,76],"show":[18],"that":[19],"there":[20,68],"are,":[21],"coarsely,":[22],"two":[23],"phase":[24,35],"transitions.":[25],"The":[26,43],"first":[27],"transition":[28,45],"is":[29,46,69],"analogous":[30],"to":[31,73],"Erd\u0151s":[33],"-R\u00e9nyi":[34],"transition,":[36],"where":[37,47,67],"complex":[40],"becomes":[41],"connected.":[42],"second":[44],"all":[48],"other":[50],"groups":[52],"are":[53],"computed":[54],"correctly":[55],"(almost":[56],"simultaneously).":[57],"Our":[58],"calculations":[59],"also":[60],"suggest":[61],"finer":[63],"measurement":[64],"scales,":[66],"further":[71],"refinement":[72],"this":[74],"picture":[75],"separation":[77],"between":[78],"different":[79],"groups.":[81],"\u00a9":[82],"2016":[83],"Wiley":[84],"Periodicals,":[85],"Inc.":[86],"Random":[87],"Struct.":[88],"Alg.,":[89],"51,":[90],"14\u201351,":[91],"2017":[92]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2019-07-30T00:00:00"}
