{"id":"https://openalex.org/W4390013332","doi":"https://doi.org/10.1017/s0963548323000469","title":"Percolation on irregular high-dimensional product graphs","display_name":"Percolation on irregular high-dimensional product graphs","publication_year":2023,"publication_date":"2023-12-20","ids":{"openalex":"https://openalex.org/W4390013332","doi":"https://doi.org/10.1017/s0963548323000469"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548323000469","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1017/s0963548323000469","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9C661CF2B121D064C55CED72C351C2B5/S0963548323000469a.pdf/div-class-title-percolation-on-irregular-high-dimensional-product-graphs-div.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9C661CF2B121D064C55CED72C351C2B5/S0963548323000469a.pdf/div-class-title-percolation-on-irregular-high-dimensional-product-graphs-div.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081714572","display_name":"Sahar Diskin","orcid":"https://orcid.org/0000-0002-5586-8152"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Sahar Diskin","raw_affiliation_strings":["School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel and","School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel and","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028299034","display_name":"Joshua Erde","orcid":"https://orcid.org/0000-0003-1129-4270"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Joshua Erde","raw_affiliation_strings":["Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002103922","display_name":"Mihyun Kang","orcid":"https://orcid.org/0000-0001-8729-2779"},"institutions":[{"id":"https://openalex.org/I4092182","display_name":"Graz University of Technology","ror":"https://ror.org/00d7xrm67","country_code":"AT","type":"education","lineage":["https://openalex.org/I4092182"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Mihyun Kang","raw_affiliation_strings":["Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria"],"raw_orcid":"https://orcid.org/0000-0001-8729-2779","affiliations":[{"raw_affiliation_string":"Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria","institution_ids":["https://openalex.org/I4092182"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008556299","display_name":"Michael Krivelevich","orcid":"https://orcid.org/0000-0003-2357-4982"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Michael Krivelevich","raw_affiliation_strings":["School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel and","School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel"],"raw_orcid":"https://orcid.org/0000-0003-2357-4982","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel and","institution_ids":["https://openalex.org/I16391192"]},{"raw_affiliation_string":"School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5081714572"],"corresponding_institution_ids":["https://openalex.org/I16391192"],"apc_list":null,"apc_paid":null,"fwci":1.5832,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.81979411,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"33","issue":"3","first_page":"377","last_page":"403"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":1.0,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6711968183517456},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.6455241441726685},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6093584299087524},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.5629284381866455},{"id":"https://openalex.org/keywords/graph-product","display_name":"Graph product","score":0.5614919066429138},{"id":"https://openalex.org/keywords/isoperimetric-inequality","display_name":"Isoperimetric inequality","score":0.5085519552230835},{"id":"https://openalex.org/keywords/symmetric-graph","display_name":"Symmetric graph","score":0.4935084581375122},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.464252769947052},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.4360713064670563},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.4353310763835907},{"id":"https://openalex.org/keywords/treewidth","display_name":"Treewidth","score":0.421225368976593},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.4058065116405487},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.39979517459869385},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.3378748595714569},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.14751535654067993}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6711968183517456},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.6455241441726685},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6093584299087524},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.5629284381866455},{"id":"https://openalex.org/C68103157","wikidata":"https://www.wikidata.org/wiki/Q569347","display_name":"Graph product","level":5,"score":0.5614919066429138},{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.5085519552230835},{"id":"https://openalex.org/C14201764","wikidata":"https://www.wikidata.org/wiki/Q1205074","display_name":"Symmetric graph","level":5,"score":0.4935084581375122},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.464252769947052},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.4360713064670563},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.4353310763835907},{"id":"https://openalex.org/C132569581","wikidata":"https://www.wikidata.org/wiki/Q5067368","display_name":"Treewidth","level":5,"score":0.421225368976593},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.4058065116405487},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.39979517459869385},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.3378748595714569},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.14751535654067993},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1017/s0963548323000469","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1017/s0963548323000469","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9C661CF2B121D064C55CED72C351C2B5/S0963548323000469a.pdf/div-class-title-percolation-on-irregular-high-dimensional-product-graphs-div.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/cf20301f-00ec-44e2-a4d2-e39c78de6672","is_oa":true,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=85181445986&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"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":"Diskin, S, Erde, J, Kang, M & Krivelevich, M 2024, 'Percolation on irregular high-dimensional product graphs', Combinatorics Probability and Computing, vol. 33, no. 3, pp. 377-403. https://doi.org/10.1017/S0963548323000469","raw_type":"article"},{"id":"pmh:oai:pure.atira.dk:publications/cf20301f-00ec-44e2-a4d2-e39c78de6672","is_oa":true,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/cf20301f-00ec-44e2-a4d2-e39c78de6672","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Diskin, S, Erde, J, Kang, M & Krivelevich, M 2024, 'Percolation on irregular high-dimensional product graphs', Combinatorics Probability and Computing, vol. 33, no. 3, pp. 377-403. https://doi.org/10.1017/S0963548323000469","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1017/s0963548323000469","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1017/s0963548323000469","pdf_url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/9C661CF2B121D064C55CED72C351C2B5/S0963548323000469a.pdf/div-class-title-percolation-on-irregular-high-dimensional-product-graphs-div.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4000000059604645,"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth"}],"awards":[{"id":"https://openalex.org/G1837873513","display_name":null,"funder_award_id":"FWF P36131","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G4135731702","display_name":null,"funder_award_id":"W1230","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G6813351766","display_name":null,"funder_award_id":"FWF W1230","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"}],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320334164","display_name":"Simons Institute for the Theory of Computing, University of California Berkeley","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4390013332.pdf","grobid_xml":"https://content.openalex.org/works/W4390013332.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W390146837","https://openalex.org/W1551555658","https://openalex.org/W1610677200","https://openalex.org/W1989844253","https://openalex.org/W2000630284","https://openalex.org/W2026620883","https://openalex.org/W2075997628","https://openalex.org/W2336317531","https://openalex.org/W2769174420","https://openalex.org/W3209196274","https://openalex.org/W4211192810","https://openalex.org/W4241669766","https://openalex.org/W4249774010","https://openalex.org/W4250226066","https://openalex.org/W4297725532","https://openalex.org/W4302344174","https://openalex.org/W6843389007"],"related_works":["https://openalex.org/W2294807589","https://openalex.org/W3184080960","https://openalex.org/W2230314777","https://openalex.org/W4291305989","https://openalex.org/W2076129127","https://openalex.org/W1974389327","https://openalex.org/W3100644252","https://openalex.org/W2532900208","https://openalex.org/W2134856394","https://openalex.org/W2294603044"],"abstract_inverted_index":{"Abstract":[0],"We":[1,18],"consider":[2],"bond":[3],"percolation":[4],"on":[5,49,165,243],"high-dimensional":[6,194,230,244],"product":[7,27,195,231,245],"graphs":[8,24,168],"$G=\\square":[9],"_{i=1}^tG^{(i)}$":[10],",":[11,40,74,110,132,248],"where":[12,75],"$\\square$":[13],"denotes":[14],"the":[15,20,22,26,30,50,54,57,61,78,82,86,96,113,118,142,150,162,166,176,180,190,210,215,221,236],"Cartesian":[16],"product.":[17],"call":[19],"$G^{(i)}$":[21],"base":[23,55,167],"and":[25,111,219,224],"graph":[28,63,218],"$G$":[29],"host":[31,83],"graph.":[32,84],"Very":[33],"recently,":[34],"Lichev":[35,127],"(":[36,128],"J.":[37,129],"Graph":[38,130],"Theory":[39,131],"99(4):651\u2013670,":[41,133],"2022)":[42],"showed":[43],"that,":[44],"under":[45],"a":[46,66,138,154,200,239],"mild":[47],"requirement":[48,143,164],"isoperimetric":[51,163],"properties":[52],"of":[53,60,81,107,117,144,153,192],"graphs,":[56,196,232],"component":[58,98,203],"structure":[59],"percolated":[62,222],"$G_p$":[64],"undergoes":[65],"phase":[67],"transition":[68],"when":[69],"$p$":[70],"is":[71,77,99,147],"around":[72],"$\\frac{1}{d}$":[73],"$d$":[76],"average":[79],"degree":[80,146],"In":[85],"supercritical":[87],"regime,":[88,182],"we":[89,121,136,159,183],"strengthen":[90],"Lichev\u2019s":[91],"result":[92],"by":[93,126,235],"showing":[94,140,187],"that":[95,141,161,188],"giant":[97],"in":[100,171,175,179,189,214,220,225,227,238],"fact":[101,226],"unique,":[102],"with":[103,204],"all":[104],"other":[105],"components":[106],"order":[108,116,156],"$o(|G|)$":[109],"determining":[112],"sharp":[114],"asymptotic":[115],"giant.":[119],"Furthermore,":[120],"answer":[122],"two":[123],"questions":[124],"posed":[125],"2022):":[134],"firstly,":[135],"provide":[137],"construction":[139],"bounded":[145],"necessary":[148],"for":[149],"likely":[151],"emergence":[152],"linear":[155],"component;":[157],"secondly,":[158],"show":[160],"can":[169,198],"be,":[170],"fact,":[172],"super-exponentially":[173],"small":[174],"dimension.":[177],"Finally,":[178],"subcritical":[181],"give":[184],"an":[185],"example":[186],"case":[191],"irregular":[193],"there":[197],"be":[199],"polynomially":[201],"large":[202],"high":[205],"probability,":[206],"very":[207],"much":[208],"unlike":[209],"quantitative":[211],"behaviour":[212],"seen":[213],"Erd\u0151s-R\u00e9nyi":[216],"random":[217],"hypercube,":[223],"any":[228],"regular":[229],"as":[233],"shown":[234],"authors":[237],"companion":[240],"paper":[241],"(Percolation":[242],"graphs.":[246],"arXiv:2209.03722":[247],"2022).":[249]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-02-07T06:11:34.122080","created_date":"2025-10-10T00:00:00"}