{"id":"https://openalex.org/W2770005279","doi":"https://doi.org/10.1017/s0963548319000191","title":"Positive association of the oriented percolation cluster in randomly oriented graphs","display_name":"Positive association of the oriented percolation cluster in randomly oriented graphs","publication_year":2019,"publication_date":"2019-07-08","ids":{"openalex":"https://openalex.org/W2770005279","doi":"https://doi.org/10.1017/s0963548319000191","mag":"2770005279"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548319000191","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548319000191","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1711.08815","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089526706","display_name":"Fran\u00e7ois Bienvenu","orcid":"https://orcid.org/0000-0002-5396-1193"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210113621","display_name":"Centre Interdisciplinaire de Recherche en Biologie","ror":"https://ror.org/01mvzn566","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I154526488","https://openalex.org/I187986737","https://openalex.org/I4210096427","https://openalex.org/I4210113621"]},{"id":"https://openalex.org/I4210147464","display_name":"Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires","ror":"https://ror.org/04hjc7403","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210147464"]},{"id":"https://openalex.org/I4387155306","display_name":"Laboratoire de Probabilit\u00e9s, Statistique et Mod\u00e9lisation","ror":"https://ror.org/02vnd0e65","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4387155306"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Fran\u00e7ois Bienvenu","raw_affiliation_strings":["Center for Interdisciplinary Research in Biology (CIRB), CNRS UMR 7241, Coll\u00e8ge de France, Paris, France","Laboratoire de Probabilit\u00e9s, Statistique et Mod\u00e9lisation (LPSM), CNRS UMR 8001, Sorbonne Universit\u00e9, Paris, France","CIRB - Centre interdisciplinaire de recherche en biologie (11 place Marcellin Berthelot 75005 Paris - France)","LPMA - Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires (France)"],"affiliations":[{"raw_affiliation_string":"Center for Interdisciplinary Research in Biology (CIRB), CNRS UMR 7241, Coll\u00e8ge de France, Paris, France","institution_ids":["https://openalex.org/I4210113621","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Laboratoire de Probabilit\u00e9s, Statistique et Mod\u00e9lisation (LPSM), CNRS UMR 8001, Sorbonne Universit\u00e9, Paris, France","institution_ids":["https://openalex.org/I4387155306","https://openalex.org/I1294671590","https://openalex.org/I39804081"]},{"raw_affiliation_string":"CIRB - Centre interdisciplinaire de recherche en biologie (11 place Marcellin Berthelot 75005 Paris - France)","institution_ids":["https://openalex.org/I4210113621"]},{"raw_affiliation_string":"LPMA - Laboratoire de Probabilit\u00e9s et Mod\u00e8les Al\u00e9atoires (France)","institution_ids":["https://openalex.org/I4210147464"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5089526706"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210113621","https://openalex.org/I4210147464","https://openalex.org/I4387155306"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.035155,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"06","first_page":"811","last_page":"815"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9987999796867371,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/mathematics","display_name":"Mathematics","score":0.6968561410903931},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6672247648239136},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6607361435890198},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.4955226182937622},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4831544756889343},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.47147512435913086},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4593226909637451},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06842893362045288}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6968561410903931},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6672247648239136},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6607361435890198},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.4955226182937622},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4831544756889343},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.47147512435913086},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4593226909637451},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06842893362045288},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1017/s0963548319000191","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548319000191","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1711.08815","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.08815","pdf_url":"https://arxiv.org/pdf/1711.08815","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:HAL:hal-01649325v1","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-01649325","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.archives-ouvertes.fr/hal-01649325","raw_type":null},{"id":"pmh:oai:HAL:hal-01649325v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01649325","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://hal.science/hal-01649325","raw_type":"info:eu-repo/semantics/preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1711.08815","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1711.08815","pdf_url":"https://arxiv.org/pdf/1711.08815","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1605754690","https://openalex.org/W1967121312","https://openalex.org/W2005443809","https://openalex.org/W2013002076","https://openalex.org/W2017722258","https://openalex.org/W2130956934","https://openalex.org/W2167595480","https://openalex.org/W2798655805","https://openalex.org/W2963160852","https://openalex.org/W4388258552"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2494523064","https://openalex.org/W2943623134","https://openalex.org/W2588219639","https://openalex.org/W2215759665","https://openalex.org/W2030292806","https://openalex.org/W2960358116","https://openalex.org/W4287727129","https://openalex.org/W3041172967","https://openalex.org/W1561721581"],"abstract_inverted_index":{"Abstract":[0],"Consider":[1],"any":[2,42,46,105],"fixed":[3],"graph":[4],"whose":[5],"edges":[6],"have":[7],"been":[8],"randomly":[9],"and":[10,13,45,50,58],"independently":[11],"oriented,":[12],"write":[14],"{":[15,53,59,112,137],"S":[16,32,44,54,60,108,113,138],"\u21dd}":[17],"to":[18,33],"indicate":[19],"that":[20,40,125],"there":[21],"is":[22,146],"an":[23,87],"oriented":[24],"path":[25],"going":[26],"from":[27],"a":[28,74],"vertex":[29,34,99],"s":[30],"\u220a":[31,118,144],"i":[35,49,56,115,117,140,143],".":[36],"Narayanan":[37],"(2016)":[38],"proved":[39],"for":[41,97,104,142],"set":[43,100,107],"two":[47],"vertices":[48],"j":[51,62],",":[52,109,120],"\u21dd":[55,61,114,139],"}":[57,63,141],"are":[64,121],"positively":[65,122],"correlated.":[66],"His":[67],"proof":[68,89],"relies":[69],"on":[70],"the":[71,91,98,102,110,126,129,135,149],"Ahlswede\u2013Daykin":[72],"inequality,":[73],"rather":[75],"advanced":[76],"tool":[77],"of":[78,90,101,128,131,134,151],"probabilistic":[79],"combinatorics.":[80],"In":[81],"this":[82],"short":[83],"note":[84],"I":[85],"give":[86],"elementary":[88],"following,":[92],"stronger":[93],"result:":[94],"writing":[95],"V":[96,119,145],"graph,":[103],"source":[106],"events":[111],"},":[116],"associated,":[123],"meaning":[124],"expectation":[127],"product":[130,150],"increasing":[132],"functionals":[133],"family":[136],"greater":[147],"than":[148],"their":[152],"expectations.":[153]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}