{"id":"https://openalex.org/W2995802452","doi":null,"title":"Left-right crossings in the Miller-Abrahams random resistor network on a Poisson point process","display_name":"Left-right crossings in the Miller-Abrahams random resistor network on a Poisson point process","publication_year":2019,"publication_date":"2019-12-16","ids":{"openalex":"https://openalex.org/W2995802452","mag":"2995802452"},"language":"en","primary_location":{"id":"mag:2995802452","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1912.07482v2","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},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/abs/1912.07482v2","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028548357","display_name":"Alessandra Faggionato","orcid":"https://orcid.org/0000-0002-6168-3517","observed_orcids":["https://orcid.org/0000-0002-6168-3517"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Alessandra Faggionato","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-6168-3517","affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039163927","display_name":"Hlafo Alfie Mimun","orcid":"https://orcid.org/0000-0001-9695-0120","observed_orcids":["https://orcid.org/0000-0001-9695-0120"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hlafo Alfie Mimun","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0001-9695-0120","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9810000061988831,"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":0.9810000061988831,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.011800000444054604,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.0012000000569969416,"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/poisson-point-process","display_name":"Poisson point process","score":0.9890000224113464},{"id":"https://openalex.org/keywords/vertex-disjoint-paths","display_name":"node-disjoint paths","score":0.7419999837875366},{"id":"https://openalex.org/keywords/phase-transitions","display_name":"phase transitions","score":0.5350000262260437},{"id":"https://openalex.org/keywords/supercritical-phase","display_name":"supercritical phase","score":0.6970000267028809},{"id":"https://openalex.org/keywords/mott-s-law","display_name":"Mott's law","score":0.7799999713897705},{"id":"https://openalex.org/keywords/amorphous-solids","display_name":"amorphous materials","score":0.6880000233650208},{"id":"https://openalex.org/keywords/electrical-conductivity","display_name":"electrical conductivity","score":0.5690000057220459},{"id":"https://openalex.org/keywords/random-graphs","display_name":"random graphs","score":0.4309999942779541},{"id":"https://openalex.org/keywords/percolation","display_name":"percolation","score":0.628000020980835}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6285902261734009},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.6082591414451599},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6077370643615723},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.4922570288181305},{"id":"https://openalex.org/C137488568","wikidata":"https://www.wikidata.org/wiki/Q5321","display_name":"Resistor","level":3,"score":0.48461899161338806},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4652690887451172},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4246806502342224},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.41762956976890564},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40735089778900146},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.3905623257160187},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37069225311279297},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.35083985328674316},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2656199336051941},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.19218716025352478},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2995802452","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1912.07482v2","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}],"best_oa_location":{"id":"mag:2995802452","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1912.07482v2","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},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W2037773093","https://openalex.org/W2075473854","https://openalex.org/W2087375600","https://openalex.org/W2143890099","https://openalex.org/W2329004779","https://openalex.org/W2783471203","https://openalex.org/W3005310653"],"related_works":["https://openalex.org/W3045593107","https://openalex.org/W7005069786","https://openalex.org/W2780022074","https://openalex.org/W2783471203","https://openalex.org/W2780810970","https://openalex.org/W3005310653","https://openalex.org/W4415345579","https://openalex.org/W3193807365","https://openalex.org/W2964291981","https://openalex.org/W4410101254"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,29,46,51,98,109,112,140,144],"Miller-Abrahams":[3],"(MA)":[4],"random":[5,26,31],"resistor":[6],"network":[7],"built":[8],"on":[9,15,62],"a\nhomogeneous":[10],"Poisson":[11],"point":[12],"process":[13],"(PPP)":[14],"$\\mathbb{R}^d$,":[16],"$d\\geq":[17],"2$.":[18],"Points":[19],"of\nthe":[20],"PPP":[21],"are":[22,100],"marked":[23],"by":[24,35,69,77,84,127],"i.i.d.":[25],"variables":[27],"and":[28,60,104],"MA":[30],"resistor\nnetwork":[32],"is":[33,124,137],"obtained":[34],"plugging":[36],"an":[37],"electrical":[38],"filament":[39,52],"between":[40,53],"any":[41],"pair":[42],"of\ndistinct":[43],"points":[44],"in":[45,57,65,72,108,118,143,149],"PPP.":[47],"The":[48,75],"conductivity":[49,81],"of":[50,115,121,131,139,146],"two":[54],"points\ndecays":[55],"exponentially":[56,132],"their":[58,63],"distance":[59],"depends":[61],"marks":[64,99],"a":[66,85,88,119],"suitable\nform":[67],"prescribed":[68],"electron":[70],"transport":[71],"amorphous":[73],"materials.":[74],"graph\nobtained":[76],"keeping":[78],"filaments":[79],"with":[80],"lower":[82,125],"bounded":[83,126],"threshold\n$\\vartheta$":[86],"exhibits":[87],"phase":[89,111],"transition":[90],"at":[91],"some":[92],"$\\vartheta_{\\rm":[93],"crit}$.":[94],"Under\nthe":[95],"assumption":[96],"that":[97,107],"nonnegative":[101],"(or":[102],"nonpositive)":[103],"bounded,":[105],"we\nshow":[106],"supercritical":[110],"maximal":[113],"number":[114],"vertex-disjoint\nleft-right":[116],"crossings":[117],"box":[120],"size":[122],"$n$":[123],"$Cn^{d-1}$":[128],"apart\nan":[129],"event":[130],"small":[133],"probability.":[134],"This":[135],"result":[136],"one":[138],"main\ningredients":[141],"entering":[142],"proof":[145],"Mott's":[147],"law":[148],"[4].":[150]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2019-12-26T00:00:00"}