{"id":"https://openalex.org/W7220928615","doi":"https://doi.org/10.48550/arxiv.2610.10097","title":"Percolation on interdependent one-dimensional long-range networks","display_name":"Percolation on interdependent one-dimensional long-range networks","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220928615","doi":"https://doi.org/10.48550/arxiv.2610.10097"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10097","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10097","pdf_url":"https://arxiv.org/pdf/2610.10097","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.10097","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5157949165","display_name":"Adar Sharabi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I164950643","display_name":"Open University of Israel","ror":"https://ror.org/027z64205","country_code":"IL","type":"education","lineage":["https://openalex.org/I164950643"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Sharabi, Adar","raw_affiliation_strings":["Department of Natural Sciences , The Open University of Israel , Ra'anana , Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Natural Sciences , The Open University of Israel , Ra'anana , Israel","institution_ids":["https://openalex.org/I164950643"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056256429","display_name":"Amir Bashan","orcid":"https://orcid.org/0000-0002-4502-3850","observed_orcids":["https://orcid.org/0000-0002-4502-3850"]},"institutions":[{"id":"https://openalex.org/I13955877","display_name":"Bar-Ilan University","ror":"https://ror.org/03kgsv495","country_code":"IL","type":"education","lineage":["https://openalex.org/I13955877"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Bashan, Amir","raw_affiliation_strings":["Department of Physics , Bar-Ilan University , Ramat Gan , Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Bar-Ilan University , Ramat Gan , Israel","institution_ids":["https://openalex.org/I13955877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033508527","display_name":"Sergey V. Buldyrev","orcid":"https://orcid.org/0000-0002-3008-1070","observed_orcids":["https://orcid.org/0000-0002-3008-1070"]},"institutions":[{"id":"https://openalex.org/I19772626","display_name":"Yeshiva University","ror":"https://ror.org/045x93337","country_code":"US","type":"education","lineage":["https://openalex.org/I19772626"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Buldyrev, Sergey V.","raw_affiliation_strings":["Department of Physics , Yeshiva University , New York , New York , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics , Yeshiva University , New York , New York , USA","institution_ids":["https://openalex.org/I19772626"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109682059","display_name":"Guy Amit","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I164950643","display_name":"Open University of Israel","ror":"https://ror.org/027z64205","country_code":"IL","type":"education","lineage":["https://openalex.org/I164950643"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Amit, Guy","raw_affiliation_strings":["Department of Natural Sciences , The Open University of Israel , Ra'anana , Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Natural Sciences , The Open University of Israel , Ra'anana , Israel","institution_ids":["https://openalex.org/I164950643"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9945999979972839,"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"}},"topics":[{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9945999979972839,"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":0.003800000064074993,"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"}},{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":9.999999747378752e-05,"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/percolation","display_name":"percolation","score":0.9710000157356262},{"id":"https://openalex.org/keywords/multiplex-networks","display_name":"multiplex networks","score":0.9340000152587891},{"id":"https://openalex.org/keywords/one-dimensional-lattice","display_name":"one-dimensional lattice","score":0.7739999890327454},{"id":"https://openalex.org/keywords/critical-threshold","display_name":"critical threshold","score":0.609000027179718},{"id":"https://openalex.org/keywords/first-order-phase-transition","display_name":"first-order phase transition","score":0.8299999833106995},{"id":"https://openalex.org/keywords/second-order-phase-transition","display_name":"second-order phase transition","score":0.9610000252723694},{"id":"https://openalex.org/keywords/interdependent-networks","display_name":"interdependent networks","score":0.6480000019073486},{"id":"https://openalex.org/keywords/tree-approximation","display_name":"tree approximation","score":0.5569999814033508}],"concepts":[{"id":"https://openalex.org/C148818006","wikidata":"https://www.wikidata.org/wiki/Q4137985","display_name":"Giant component","level":4,"score":0.8589000105857849},{"id":"https://openalex.org/C2780457167","wikidata":"https://www.wikidata.org/wiki/Q17156484","display_name":"Percolation (cognitive psychology)","level":2,"score":0.6765000224113464},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6100999712944031},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.59170001745224},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.5792999863624573},{"id":"https://openalex.org/C19768560","wikidata":"https://www.wikidata.org/wiki/Q320727","display_name":"Dependency (UML)","level":2,"score":0.5440000295639038},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.5034999847412109},{"id":"https://openalex.org/C101142422","wikidata":"https://www.wikidata.org/wiki/Q17101727","display_name":"Interdependent networks","level":3,"score":0.49970000982284546},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.49050000309944153},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.41339999437332153},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.4074000120162964},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.39809998869895935},{"id":"https://openalex.org/C152139883","wikidata":"https://www.wikidata.org/wiki/Q252973","display_name":"Mutual information","level":2,"score":0.3910999894142151},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.34940001368522644},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.3474000096321106},{"id":"https://openalex.org/C11557063","wikidata":"https://www.wikidata.org/wiki/Q900918","display_name":"Percolation theory","level":3,"score":0.34610000252723694},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3343000113964081},{"id":"https://openalex.org/C2729557","wikidata":"https://www.wikidata.org/wiki/Q7167170","display_name":"Percolation threshold","level":3,"score":0.29280000925064087},{"id":"https://openalex.org/C2781188995","wikidata":"https://www.wikidata.org/wiki/Q6934982","display_name":"Multiplex","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2890999913215637},{"id":"https://openalex.org/C104122410","wikidata":"https://www.wikidata.org/wiki/Q1416406","display_name":"Network model","level":2,"score":0.28119999170303345},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.27959999442100525}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10097","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10097","pdf_url":"https://arxiv.org/pdf/2610.10097","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":"doi:10.48550/arxiv.2610.10097","doi":"https://doi.org/10.48550/arxiv.2610.10097","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10097","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.10097","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10097","pdf_url":"https://arxiv.org/pdf/2610.10097","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/G8856604570","display_name":null,"funder_award_id":"2020255","funder_id":"https://openalex.org/F4320320950","funder_display_name":"United States-Israel Binational Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320320950","display_name":"United States-Israel Binational Science Foundation","ror":"https://ror.org/00j8z2m73"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220928615.pdf","grobid_xml":"https://content.openalex.org/works/W7220928615.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4413300131","https://openalex.org/W7077917762"],"related_works":["https://openalex.org/W1876966867","https://openalex.org/W2019819991","https://openalex.org/W2344555404","https://openalex.org/W2000374591","https://openalex.org/W2397203946","https://openalex.org/W2033192342","https://openalex.org/W3119041597","https://openalex.org/W1608224973","https://openalex.org/W2295661434","https://openalex.org/W3217669816"],"abstract_inverted_index":{"We":[0,80],"study":[1],"the":[2,111,119,130,137,140,148,163,168,176],"emergence":[3],"of":[4,14,73,93,122,139,174],"a":[5,10,20,31,70,88,155],"mutual":[6,59,149],"giant":[7,60,150],"component":[8,61,151],"in":[9,154],"multiplex":[11,104],"network":[12,105,113],"comprised":[13],"two":[15,25],"one-dimensional":[16],"long-range":[17],"networks":[18],"on":[19,27,78,85,143],"lattice.":[21],"The":[22,103],"probability":[23],"that":[24,75,136],"nodes":[26],"one":[28],"lattice,":[29],"with":[30,38,43,96],"distance":[32,44],"$r$":[33],"between":[34],"them,":[35],"are":[36],"connected":[37],"an":[39],"edge":[40],"falls":[41],"algebraically":[42],"as":[45,115],"$Cr^{-(1+\u03c3)}$,":[46],"where":[47,67],"$0":[48,53],"<":[49,54],"\u03c3<":[50],"1$":[51],"and":[52,87],"C":[55],"\\leq":[56],"1$.":[57],"A":[58],"exists":[62],"if":[63],"$C":[64],">":[65],"C_c^{\\mathrm{mul}}$,":[66],"$C_c^{\\mathrm{mul}}(\u03c3)$":[68],"is":[69,76,106,116,125,165,178],"critical":[71],"value":[72,121],"$C$":[74],"dependent":[77],"$\u03c3$.":[79,144,183],"find":[81],"rigorous":[82],"lower":[83],"bounds":[84],"$C_c^{\\mathrm{mul}}$,":[86,123],"tree":[89],"approximation":[90],"whose":[91],"estimate":[92],"$C_c^{\\mathrm{mul}}$":[94],"agrees":[95],"simulations":[97,134],"within":[98],"0.6%":[99],"for":[100,160,181],"$\u03c3\\leq":[101,146],"0.5$.":[102],"significantly":[107],"less":[108],"stable":[109],"than":[110],"single":[112],"case,":[114],"evident":[117],"by":[118],"larger":[120],"which":[124],"up":[126],"to":[127],"2.4":[128],"times":[129],"single-layer":[131],"value.":[132],"Our":[133],"indicate":[135],"order":[138,180],"transition":[141,164,177],"depends":[142],"For":[145],"0.35$":[147],"collapses":[152],"abruptly,":[153],"first-order":[156],"phase":[157],"transition,":[158],"while":[159],"$\u03c3\\geq":[161],"0.4$":[162],"continuous.":[166],"When":[167],"dependency":[169],"links":[170],"connect":[171],"random":[172],"pairs":[173],"nodes,":[175],"first":[179],"all":[182]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-09T00:00:00"}
