{"id":"https://openalex.org/W7204755618","doi":"https://doi.org/10.48550/arxiv.2608.27474","title":"Nonlocality of Cover-Time Changes Under Edge Addition","display_name":"Nonlocality of Cover-Time Changes Under Edge Addition","publication_year":2026,"publication_date":"2026-08-19","ids":{"openalex":"https://openalex.org/W7204755618","doi":"https://doi.org/10.48550/arxiv.2608.27474"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.27474","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27474","pdf_url":"https://arxiv.org/pdf/2608.27474","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/2608.27474","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147332261","display_name":"Ian Meng Si","orcid":"https://orcid.org/0009-0006-9406-9579","observed_orcids":["https://orcid.org/0009-0006-9406-9579"]},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Si, Ian Meng","raw_affiliation_strings":["Department of Statistics , University of California , Berkeley , Berkeley , CA 94720 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics , University of California , Berkeley , Berkeley , CA 94720 , USA","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5147332261"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9779999852180481,"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":0.9779999852180481,"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/T13500","display_name":"Probability and Statistical Research","score":0.006500000134110451,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.002899999963119626,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/cover-time","display_name":"cover time","score":0.8830000162124634},{"id":"https://openalex.org/keywords/simple-random-walk","display_name":"simple random walk","score":0.8610000014305115},{"id":"https://openalex.org/keywords/edge-addition","display_name":"edge addition","score":0.7269999980926514},{"id":"https://openalex.org/keywords/nonlocality","display_name":"nonlocality","score":0.8539999723434448},{"id":"https://openalex.org/keywords/inclusion-exclusion-principle","display_name":"inclusion-exclusion","score":0.9169999957084656},{"id":"https://openalex.org/keywords/effective-resistance","display_name":"effective resistance","score":0.878000020980835},{"id":"https://openalex.org/keywords/conductance","display_name":"conductance","score":0.671999990940094},{"id":"https://openalex.org/keywords/graph-contraction","display_name":"graph contraction","score":0.7319999933242798},{"id":"https://openalex.org/keywords/occupation-measures","display_name":"occupation measures","score":0.5210000276565552},{"id":"https://openalex.org/keywords/random-walks-on-graphs","display_name":"random walks on graphs","score":0.5559999942779541}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7656999826431274},{"id":"https://openalex.org/C138622882","wikidata":"https://www.wikidata.org/wiki/Q7269079","display_name":"Quantum nonlocality","level":4,"score":0.6777999997138977},{"id":"https://openalex.org/C527412718","wikidata":"https://www.wikidata.org/wiki/Q855395","display_name":"Interpretation (philosophy)","level":2,"score":0.5425000190734863},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.536899983882904},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.5134999752044678},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5087000131607056},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.49239999055862427},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4510999917984009},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.44119998812675476},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.4223000109195709},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4133000075817108},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4099999964237213},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4041999876499176},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.38449999690055847},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.3652999997138977},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36309999227523804},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.3490000069141388},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.3398999869823456},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.3095000088214874},{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C121932024","wikidata":"https://www.wikidata.org/wiki/Q5159376","display_name":"Conductance","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28029999136924744},{"id":"https://openalex.org/C14103023","wikidata":"https://www.wikidata.org/wiki/Q11681459","display_name":"Pairing","level":3,"score":0.2705000042915344},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2533000111579895}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.27474","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27474","pdf_url":"https://arxiv.org/pdf/2608.27474","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.2608.27474","doi":"https://doi.org/10.48550/arxiv.2608.27474","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.27474","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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.27474","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.27474","pdf_url":"https://arxiv.org/pdf/2608.27474","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204755618.pdf","grobid_xml":"https://content.openalex.org/works/W7204755618.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1986269714","https://openalex.org/W2019415463","https://openalex.org/W2057596055","https://openalex.org/W2064087447","https://openalex.org/W2068008593","https://openalex.org/W2078394884","https://openalex.org/W2156184725","https://openalex.org/W2167064216","https://openalex.org/W2170807097","https://openalex.org/W4230376356","https://openalex.org/W4247804722"],"related_works":["https://openalex.org/W2142468746","https://openalex.org/W2182235028","https://openalex.org/W7096337108","https://openalex.org/W3201913500","https://openalex.org/W2997342291","https://openalex.org/W7052050339","https://openalex.org/W2953360466","https://openalex.org/W2589732210","https://openalex.org/W2261367360","https://openalex.org/W1847535063"],"abstract_inverted_index":{"Let":[0],"$G$":[1],"be":[2,10,16],"a":[3,11,17,66,126,146,180],"finite":[4],"connected":[5],"simple":[6,31],"graph,":[7],"let":[8,14],"$uv$":[9,35],"nonedge,":[12],"and":[13,106,130,141,158,178],"$s$":[15],"starting":[18,176],"vertex.":[19],"We":[20,121],"study":[21],"the":[22,26,53,99,103,107,150,155,186],"exact":[23,49],"change":[24,182],"in":[25],"expected":[27,151],"cover":[28],"time":[29],"of":[30,134,149,154,183],"random":[32],"walk":[33],"when":[34],"is":[36,65,145,162,172],"inserted.":[37],"A":[38,165],"killed":[39],"Green":[40],"matrix":[41],"update,":[42],"combined":[43],"with":[44,125,167],"target-set":[45],"inclusion-exclusion,":[46],"gives":[47],"an":[48,131],"formula":[50],"using":[51],"only":[52],"original":[54],"graph.":[55],"The":[56,95,111],"response":[57],"can":[58],"have":[59,92,114],"either":[60],"sign.":[61],"Our":[62],"main":[63],"result":[64,124],"nonlocality":[67,118],"theorem.":[68],"For":[69],"every":[70],"radius":[71],"$r\\geq":[72],"1$,":[73],"we":[74],"construct":[75],"two":[76,112,168],"marked":[77,101,104],"configurations":[78],"whose":[79,88],"ambient-degree-labelled":[80],"radius-$r$":[81],"neighbourhoods":[82],"at":[83],"$s,u,v$":[84],"are":[85],"isomorphic":[86],"but":[87],"fixed-start":[89],"cover-time":[90],"responses":[91],"opposite":[93],"signs.":[94],"construction":[96],"also":[97],"matches":[98],"three":[100],"degrees,":[102],"distance,":[105],"effective":[108],"resistance":[109],"$R_{uv}$.":[110],"graphs":[113],"different":[115],"orders;":[116],"equal-order":[117],"remains":[119],"open.":[120],"complement":[122],"this":[123],"conductance":[127],"interpolation":[128],"theorem":[129],"occupation":[132,153],"interpretation":[133],"its":[135,159],"high-conductance":[136],"coefficient.":[137],"After":[138],"contracting":[139],"$u$":[140],"$v$,":[142],"that":[143],"coefficient":[144],"positive":[147],"multiple":[148],"pre-cover":[152],"contracted":[156],"vertex,":[157],"zero":[160],"case":[161],"classified":[163],"exactly.":[164],"path":[166],"pendant":[169],"insertion":[170],"endpoints":[171],"solved":[173],"for":[174],"all":[175],"vertices":[177],"shows":[179],"sharp":[181],"sign":[184],"across":[185],"start":[187],"set.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-01T00:00:00"}
