{"id":"https://openalex.org/W4250591328","doi":"https://doi.org/10.1002/rsa.20265","title":"Linear lower bounds for \u03b4c(p) for a class of 2D self\u2010destructive percolation models","display_name":"Linear lower bounds for \u03b4c(p) for a class of 2D self\u2010destructive percolation models","publication_year":2009,"publication_date":"2009-02-02","ids":{"openalex":"https://openalex.org/W4250591328","doi":"https://doi.org/10.1002/rsa.20265"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.20265","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,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0711.3563v1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101680227","display_name":"Jacob van den Berg","orcid":"https://orcid.org/0000-0002-4552-2203"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832"]},{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"J. van den Berg","raw_affiliation_strings":["Department of Mathematics, CWI and Vrije Universiteit, Amsterdam, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, CWI and Vrije Universiteit, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I1341640284","https://openalex.org/I865915315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028384518","display_name":"Bernardo N. B. de Lima","orcid":"https://orcid.org/0000-0002-5318-0389"},"institutions":[{"id":"https://openalex.org/I110200422","display_name":"Universidade Federal de Minas Gerais","ror":"https://ror.org/0176yjw32","country_code":"BR","type":"education","lineage":["https://openalex.org/I110200422"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"B.N.B. de Lima","raw_affiliation_strings":["Departamento de Matema\u0301tica, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil"],"affiliations":[{"raw_affiliation_string":"Departamento de Matema\u0301tica, Universidade Federal de Minas Gerais, Belo Horizonte, Brazil","institution_ids":["https://openalex.org/I110200422"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101680227"],"corresponding_institution_ids":["https://openalex.org/I1341640284","https://openalex.org/I865915315"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330,"provenance":"doaj"},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":4,"citation_normalized_percentile":{"value":0.504291,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":77,"max":79},"biblio":{"volume":"34","issue":"4","first_page":"520","last_page":"526"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Scaling Limits of Interacting Particle Systems","score":0.9999,"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/T11152","display_name":"Scaling Limits of Interacting Particle Systems","score":0.9999,"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/T11716","display_name":"Random Matrix Theory and Its Applications","score":0.995,"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"}},{"id":"https://openalex.org/T12056","display_name":"Bayesian Monte Carlo Methods in Scientific Inference","score":0.9944,"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/square-lattice","display_name":"Square lattice","score":0.7976333},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5754182},{"id":"https://openalex.org/keywords/percolation-models","display_name":"Percolation Models","score":0.550692},{"id":"https://openalex.org/keywords/hexagonal-lattice","display_name":"Hexagonal lattice","score":0.49519053},{"id":"https://openalex.org/keywords/percolation","display_name":"Percolation (cognitive psychology)","score":0.47313324},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.45397782},{"id":"https://openalex.org/keywords/percolation-theory","display_name":"Percolation theory","score":0.43171918}],"concepts":[{"id":"https://openalex.org/C2777620828","wikidata":"https://www.wikidata.org/wiki/Q7582067","display_name":"Square lattice","level":3,"score":0.7976333},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6865373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5883917},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5754182},{"id":"https://openalex.org/C90626534","wikidata":"https://www.wikidata.org/wiki/Q4523381","display_name":"Hexagonal lattice","level":3,"score":0.49519053},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4822986},{"id":"https://openalex.org/C2780457167","wikidata":"https://www.wikidata.org/wiki/Q17156484","display_name":"Percolation (cognitive psychology)","level":2,"score":0.47313324},{"id":"https://openalex.org/C2729557","wikidata":"https://www.wikidata.org/wiki/Q7167170","display_name":"Percolation threshold","level":3,"score":0.45600757},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.45397782},{"id":"https://openalex.org/C11557063","wikidata":"https://www.wikidata.org/wiki/Q900918","display_name":"Percolation theory","level":3,"score":0.43171918},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40395695},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.25755423},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23585165},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.22429296},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.13634202},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11351037},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C169760540","wikidata":"https://www.wikidata.org/wiki/Q207011","display_name":"Neuroscience","level":1,"score":0.0},{"id":"https://openalex.org/C155355069","wikidata":"https://www.wikidata.org/wiki/Q575224","display_name":"Antiferromagnetism","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C51329190","wikidata":"https://www.wikidata.org/wiki/Q1076349","display_name":"Ising model","level":2,"score":0.0},{"id":"https://openalex.org/C69990965","wikidata":"https://www.wikidata.org/wiki/Q65402698","display_name":"Electrical resistivity and conductivity","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1002/rsa.20265","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,"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":null,"is_accepted":false,"is_published":false},{"is_oa":true,"landing_page_url":null,"pdf_url":"https://arxiv.org/pdf/0711.3563v1.pdf","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false}],"best_oa_location":{"is_oa":true,"landing_page_url":null,"pdf_url":"https://arxiv.org/pdf/0711.3563v1.pdf","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":["Cornell University"],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false},"sustainable_development_goals":[{"score":0.61,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":3,"referenced_works":["https://openalex.org/W2522234507","https://openalex.org/W4250226066","https://openalex.org/W4302344174"],"related_works":["https://openalex.org/W45257362","https://openalex.org/W3042760486","https://openalex.org/W2146411576","https://openalex.org/W2135100458","https://openalex.org/W2086354835","https://openalex.org/W2078697937","https://openalex.org/W2074855102","https://openalex.org/W2065549434","https://openalex.org/W2024541258","https://openalex.org/W2023077343"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"self\u2010destructive":[2],"percolation":[3,10,179,188],"model":[4,70,84],"is":[5,37,119],"defined":[6],"as":[7],"follows:":[8],"Consider":[9],"with":[11],"parameter":[12],"p":[13,15,50,105,117,124,126,160,163,165],">":[14],"c":[16,48,103,115,127,158,166],".":[17,111,128],"Remove":[18],"the":[19,53,66,82,86,130,181,190,197],"infinite":[20,62],"occupied":[21,63],"cluster.":[22],"Finally,":[23],"give":[24],"each":[25,31],"vertex":[26],"(or,":[27],"for":[28,81,156,168],"bond":[29,178],"percolation,":[30],"edge)":[32],"that":[33,101,144],"at":[34,120],"this":[35],"stage":[36],"vacant,":[38],"an":[39,61],"extra":[40],"chance":[41],"\u03b4":[42,47,102,114,157],"to":[43,59,150],"become":[44],"occupied.":[45],"Let":[46],"(":[49,104,116,159],")":[51,106,118,161,167],"be":[52,147],"minimal":[54],"value":[55],"of":[56,173,196],"\u03b4,":[57],"needed":[58],"obtain":[60,151],"cluster":[64],"in":[65,123],"final":[67],"configuration.":[68],"This":[69],"was":[71],"introduced":[72],"by":[73,133],"van":[74,134],"den":[75,135],"Berg":[76,136],"and":[77,137,183,186],"Brouwer.":[78],"They":[79],"showed,":[80],"site":[83,187],"on":[85,180,189],"square":[87,182,198],"lattice":[88,192],"(and":[89],"a":[90,97,169],"few":[91],"other":[92],"2":[93,174],"D":[94,175],"lattices":[95],"satisfying":[96],"special":[98],"technical":[99],"condition)":[100],"\u2265":[107],"${(p-p_{c})\\over":[108],"{p}}":[109],"$":[110],"In":[112],"particular,":[113],"least":[121],"linear":[122,153],"\u2212":[125],"Although":[129],"arguments":[131],"used":[132],"Brouwer":[138],"look":[139],"very":[140],"lattice\u2010specific,":[141],"we":[142],"show":[143],"they":[145],"can":[146],"suitably":[148],"modified":[149],"similar":[152],"lower":[154],"bounds":[155],"(with":[162],"near":[164],"much":[170],"larger":[171],"class":[172],"lattices,":[176,185],"including":[177],"triangular":[184],"star":[191],"(or":[193],"matching":[194],"lattice)":[195],"lattice.":[199],"\u00a9":[200],"2009":[201,208],"Wiley":[202],"Periodicals,":[203],"Inc.":[204],"Random":[205],"Struct.":[206],"Alg.,":[207]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W4250591328","counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2024-09-19T19:09:22.662514","created_date":"2022-05-12"}
