{"id":"https://openalex.org/W7225396015","doi":"https://doi.org/10.5281/zenodo.24023209","title":"Nonuniqueness of site percolation on nonamenable quasi-transitive graphs","display_name":"Nonuniqueness of site percolation on nonamenable quasi-transitive graphs","publication_year":2026,"publication_date":"2026-11-06","ids":{"openalex":"https://openalex.org/W7225396015","doi":"https://doi.org/10.5281/zenodo.24023209"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24023209","doi":"https://doi.org/10.5281/zenodo.24023209","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24023209","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24023209","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064867350","display_name":"Yan Ru Pei","orcid":"https://orcid.org/0000-0002-6999-3691","observed_orcids":["https://orcid.org/0000-0002-6999-3691"]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Pei, Yan Ru","raw_affiliation_strings":["University of California San Diego"],"raw_orcid":"https://orcid.org/0000-0002-6999-3691","affiliations":[{"raw_affiliation_string":"University of California San Diego","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064867350"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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":0.9907000064849854,"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":0.9907000064849854,"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":0.0020000000949949026,"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.001500000013038516,"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/site-percolation","display_name":"site percolation","score":0.9750000238418579},{"id":"https://openalex.org/keywords/quasi-transitive-graphs","display_name":"quasi-transitive graphs","score":0.9990000128746033},{"id":"https://openalex.org/keywords/critical-probability","display_name":"critical probability","score":0.7889999747276306},{"id":"https://openalex.org/keywords/bernoulli-percolation","display_name":"Bernoulli percolation","score":0.7979999780654907},{"id":"https://openalex.org/keywords/bond-percolation","display_name":"bond percolation","score":0.7350000143051147},{"id":"https://openalex.org/keywords/cut-vertices","display_name":"cut vertices","score":0.6650000214576721},{"id":"https://openalex.org/keywords/locally-finite-graphs","display_name":"locally finite graphs","score":0.5199999809265137}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7283999919891357},{"id":"https://openalex.org/C201958917","wikidata":"https://www.wikidata.org/wiki/Q1367055","display_name":"Unimodular matrix","level":2,"score":0.6603000164031982},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5174999833106995},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5088000297546387},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4819999933242798},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.4634000062942505},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.41999998688697815},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.40310001373291016},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4000000059604645},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.38690000772476196},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.3603000044822693},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.35249999165534973},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3483999967575073},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3352999985218048},{"id":"https://openalex.org/C2780457167","wikidata":"https://www.wikidata.org/wiki/Q17156484","display_name":"Percolation (cognitive psychology)","level":2,"score":0.3190999925136566},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.3188000023365021},{"id":"https://openalex.org/C2729557","wikidata":"https://www.wikidata.org/wiki/Q7167170","display_name":"Percolation threshold","level":3,"score":0.3084999918937683},{"id":"https://openalex.org/C110729354","wikidata":"https://www.wikidata.org/wiki/Q185478","display_name":"Countable set","level":2,"score":0.296999990940094},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2605000138282776},{"id":"https://openalex.org/C177634923","wikidata":"https://www.wikidata.org/wiki/Q17005777","display_name":"Continuum percolation theory","level":5,"score":0.2578999996185303},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.2524000108242035}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24023209","doi":"https://doi.org/10.5281/zenodo.24023209","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24023209","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.24023210","doi":"https://doi.org/10.5281/zenodo.24023210","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24023210","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.24023209","doi":"https://doi.org/10.5281/zenodo.24023209","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24023209","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7224992435","https://openalex.org/W7225432295","https://openalex.org/W2767306879","https://openalex.org/W7225016644","https://openalex.org/W2398326034","https://openalex.org/W3105496190","https://openalex.org/W7099331138","https://openalex.org/W2939811869","https://openalex.org/W3196309622","https://openalex.org/W2137147352"],"abstract_inverted_index":{"Benjamini":[0],"and":[1,50,114,126],"Schramm":[2],"conjectured":[3],"in":[4,21,51],"1996":[5],"that":[6],"site":[7,27,72,128],"percolation":[8,28,70,73],"on":[9,29,43,74],"every":[10,30,62],"nonamenable":[11,34],"quasi-transitive":[12,35,133],"graph":[13],"has":[14],"p_c":[15,45],"<":[16,46],"p_u.":[17],"We":[18],"prove":[19],"this":[20,78],"Hutchcroft's":[22],"operator":[23,40],"form:":[24],"for":[25],"Bernoulli":[26],"connected,":[31],"locally":[32],"finite,":[33],"graph,":[36,77],"the":[37,52,75,107],"critical":[38],"two-point":[39],"is":[41,71],"bounded":[42],"\u2113\u00b2,":[44],"p_{2\u21922}":[47],"\u2264":[48],"p_u,":[49],"standard":[53],"monotone":[54],"coupling":[55],"infinitely":[56],"many":[57],"infinite":[58],"clusters":[59],"coexist":[60],"at":[61],"parameter":[63],"of":[64],"a":[65,96,103,112],"nondegenerate":[66],"interval.":[67],"Since":[68],"bond":[69,82],"line":[76],"contains":[79],"OpenAI's":[80,90],"recent":[81],"theorem.":[83],"For":[84,120],"unimodular":[85],"automorphism":[86],"groups":[87,122],"we":[88,123],"adapt":[89],"proof:":[91],"cut":[92],"vertices":[93],"replace":[94],"bridges,":[95],"pruning":[97],"lemma":[98],"handles":[99],"retained":[100],"contact":[101],"vertices,":[102],"rejection":[104],"step":[105],"controls":[106],"junctions":[108],"created":[109],"by":[110],"opening":[111],"vertex,":[113],"pivotal":[115],"corridors":[116],"become":[117],"induced":[118],"paths.":[119],"nonunimodular":[121],"extend":[124],"Tran":[125],"Nguyen's":[127],"argument":[129],"from":[130],"vertex-transitive":[131],"to":[132],"graphs.":[134]},"counts_by_year":[],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-11-07T00:00:00"}
