{"id":"https://openalex.org/W1977827673","doi":"https://doi.org/10.1137/090775361","title":"Interlacings for Random Walks on Weighted Graphs and the Interchange Process","display_name":"Interlacings for Random Walks on Weighted Graphs and the Interchange Process","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W1977827673","doi":"https://doi.org/10.1137/090775361","mag":"1977827673"},"language":"en","primary_location":{"id":"doi:10.1137/090775361","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090775361","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/0906.1716","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069071519","display_name":"A. B. Dieker","orcid":null},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. B. Dieker","raw_affiliation_strings":["ton.dieker@isye.gatech.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"ton.dieker@isye.gatech.edu#TAB#","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5069071519"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":3.1892,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.91310461,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"1","first_page":"191","last_page":"206"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9973000288009644,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9970999956130981,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8863401412963867},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7518622279167175},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7495563626289368},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"Spectral gap","score":0.6754617691040039},{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.6295971274375916},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.46070969104766846},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.45472800731658936},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.43780308961868286},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.418533056974411},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4120534360408783},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12462493777275085},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.058264583349227905}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8863401412963867},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7518622279167175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7495563626289368},{"id":"https://openalex.org/C2778114796","wikidata":"https://www.wikidata.org/wiki/Q7575194","display_name":"Spectral gap","level":2,"score":0.6754617691040039},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.6295971274375916},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.46070969104766846},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.45472800731658936},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.43780308961868286},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.418533056974411},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4120534360408783},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12462493777275085},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.058264583349227905},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/090775361","is_oa":false,"landing_page_url":"https://doi.org/10.1137/090775361","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:0906.1716","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0906.1716","pdf_url":"https://arxiv.org/pdf/0906.1716","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,"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":"pmh:oai:CiteSeerX.psu:10.1.1.249.5380","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.249.5380","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0906.1716v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.740.2451","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.740.2451","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0906.1716.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:0906.1716","is_oa":true,"landing_page_url":"http://arxiv.org/abs/0906.1716","pdf_url":"https://arxiv.org/pdf/0906.1716","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,"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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.6200000047683716}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W247697463","https://openalex.org/W1518468345","https://openalex.org/W1551177513","https://openalex.org/W1596709027","https://openalex.org/W1600293573","https://openalex.org/W1834517917","https://openalex.org/W1977827673","https://openalex.org/W2022507394","https://openalex.org/W2030409851","https://openalex.org/W2031769269","https://openalex.org/W2056389572","https://openalex.org/W2058006306","https://openalex.org/W2068785829","https://openalex.org/W2069626659","https://openalex.org/W2148780152","https://openalex.org/W2318438148","https://openalex.org/W2503354009","https://openalex.org/W2610857016","https://openalex.org/W2914659449","https://openalex.org/W2914999726","https://openalex.org/W3102701461","https://openalex.org/W4214684581","https://openalex.org/W4230266844","https://openalex.org/W4238591275"],"related_works":["https://openalex.org/W1597743604","https://openalex.org/W2038723108","https://openalex.org/W3103885756","https://openalex.org/W2033630974","https://openalex.org/W4300899577","https://openalex.org/W2560376394","https://openalex.org/W822020258","https://openalex.org/W4299378864","https://openalex.org/W2953336627","https://openalex.org/W3099059030"],"abstract_inverted_index":{"We":[0,28,62],"study":[1],"Aldous's":[2,44,80,121],"conjecture":[3,31,45,81],"that":[4,40],"the":[5,9,18,22,33,64,75,128,133],"spectral":[6,19],"gap":[7,20],"of":[8,21,35,53,74,86,108],"interchange":[10],"process":[11],"on":[12,25,56],"a":[13,30,83],"weighted":[14,57,87,106],"undirected":[15],"graph":[16],"equals":[17],"random":[23,54],"walk":[24],"this":[26,41],"graph.":[27],"present":[29,134],"in":[32,132],"form":[34],"an":[36,48,72],"inequality":[37,42,66],"and":[38,111,116,125],"prove":[39,63,79],"implies":[43],"by":[46],"combining":[47],"interlacing":[49],"result":[50],"for":[51,67,82],"Laplacians":[52],"walks":[55],"graphs":[58,95,103],"with":[59,96,104],"representation":[60],"theory.":[61],"conjectured":[65],"several":[68,105],"important":[69],"instances.":[70],"As":[71],"application":[73],"developed":[76,131],"theory,":[77],"we":[78],"large":[84],"class":[85],"graphs,":[88,93,101],"which":[89],"includes":[90],"all":[91,94,112],"wheel":[92],"four":[97],"vertices,":[98],"certain":[99,102],"nonplanar":[100],"cycles":[107],"arbitrary":[109],"length,":[110],"trees.":[113],"Caputo,":[114],"Liggett,":[115],"Richthammer":[117],"have":[118],"recently":[119],"resolved":[120],"conjecture,":[122],"after":[123],"independently":[124],"simultaneously":[126],"discovering":[127],"key":[129],"ideas":[130],"paper.":[135]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2013,"cited_by_count":3}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
