{"id":"https://openalex.org/W2976698830","doi":"https://doi.org/10.1137/20m1339246","title":"Random Walks on Dense Graphs and Graphons","display_name":"Random Walks on Dense Graphs and Graphons","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2976698830","doi":"https://doi.org/10.1137/20m1339246","mag":"2976698830"},"language":"en","primary_location":{"id":"doi:10.1137/20m1339246","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1339246","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1909.11776","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005999427","display_name":"Julien Petit","orcid":"https://orcid.org/0000-0002-7846-1275"},"institutions":[{"id":"https://openalex.org/I149768937","display_name":"University of Namur","ror":"https://ror.org/03d1maw17","country_code":"BE","type":"education","lineage":["https://openalex.org/I149768937"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Julien Petit","raw_affiliation_strings":["Universit\u00e9 de namur >  >  >  >"],"raw_orcid":"https://orcid.org/0000-0002-7846-1275","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de namur >  >  >  >","institution_ids":["https://openalex.org/I149768937"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034372799","display_name":"Renaud Lambiotte","orcid":"https://orcid.org/0000-0002-0583-4595"},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Renaud Lambiotte","raw_affiliation_strings":["University of Oxford"],"raw_orcid":"https://orcid.org/0000-0002-0583-4595","affiliations":[{"raw_affiliation_string":"University of Oxford","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001066958","display_name":"Timot\u00e9o Carletti","orcid":"https://orcid.org/0000-0003-2596-4503"},"institutions":[{"id":"https://openalex.org/I149768937","display_name":"University of Namur","ror":"https://ror.org/03d1maw17","country_code":"BE","type":"education","lineage":["https://openalex.org/I149768937"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Timoteo Carletti","raw_affiliation_strings":["Universit\u00e9 de namur >  >  >  >"],"raw_orcid":"https://orcid.org/0000-0003-2596-4503","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de namur >  >  >  >","institution_ids":["https://openalex.org/I149768937"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2667,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.76045528,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"81","issue":"6","first_page":"2323","last_page":"2345"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9993000030517578,"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/T10064","display_name":"Complex Network Analysis Techniques","score":0.9991000294685364,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/random-walk","display_name":"Random walk","score":0.595496416091919},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5929412245750427},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.590339183807373},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.542573094367981},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5173520445823669},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.5008494853973389},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.41782906651496887},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.41449931263923645},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4142100512981415},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.41045740246772766},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3832918405532837},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3636731505393982},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.28036656975746155},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1677585244178772},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14401841163635254},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.09580063819885254}],"concepts":[{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.595496416091919},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5929412245750427},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.590339183807373},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.542573094367981},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5173520445823669},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5008494853973389},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.41782906651496887},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.41449931263923645},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4142100512981415},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.41045740246772766},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3832918405532837},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3636731505393982},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.28036656975746155},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1677585244178772},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14401841163635254},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.09580063819885254},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/20m1339246","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1339246","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1909.11776","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.11776","pdf_url":"https://arxiv.org/pdf/1909.11776","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},{"id":"mag:2976698830","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1909.11776v2","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:ora.ox.ac.uk:uuid:ab5ccce8-1f8f-4ef4-b4d0-a320ee832686","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:ab5ccce8-1f8f-4ef4-b4d0-a320ee832686","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements","raw_type":"Journal article"},{"id":"pmh:oai:pure.unamur.be:openaire_cris_publications/8c6589cb-3057-495f-806e-b8b649d58bfb","is_oa":false,"landing_page_url":"https://epubs.siam.org/doi/10.1137/20M1339246","pdf_url":null,"source":{"id":"https://openalex.org/S4406922457","display_name":"Repository of the University of Namur","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"PETIT, J, Lambiotte, R & Carletti, T 2021, 'Random walks on dense graphs and graphons', SIAM journal on applied mathematics, vol. 81, no. 6, pp. 2323-2345. https://doi.org/10.1137/20m1339246","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:pure.unamur.be:publications/8c6589cb-3057-495f-806e-b8b649d58bfb","is_oa":false,"landing_page_url":"https://researchportal.unamur.be/en/publications/8c6589cb-3057-495f-806e-b8b649d58bfb","pdf_url":null,"source":{"id":"https://openalex.org/S4406922457","display_name":"Repository of the University of Namur","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"PETIT, J, Lambiotte, R & Carletti, T 2021, 'Random walks on dense graphs and graphons', SIAM journal on applied mathematics, vol. 81, no. 6, pp. 2323-2345. https://doi.org/10.1137/20m1339246","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"doi:10.48550/arxiv.1909.11776","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.11776","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1909.11776","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.11776","pdf_url":"https://arxiv.org/pdf/1909.11776","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2976698830.pdf","grobid_xml":"https://content.openalex.org/works/W2976698830.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W273178449","https://openalex.org/W1532790179","https://openalex.org/W1533473741","https://openalex.org/W1606157354","https://openalex.org/W1796173830","https://openalex.org/W1883408324","https://openalex.org/W1964778716","https://openalex.org/W1968878530","https://openalex.org/W1989368986","https://openalex.org/W1991709920","https://openalex.org/W2002276939","https://openalex.org/W2012792957","https://openalex.org/W2014478203","https://openalex.org/W2029972636","https://openalex.org/W2044988896","https://openalex.org/W2066636486","https://openalex.org/W2081696668","https://openalex.org/W2082734581","https://openalex.org/W2102907934","https://openalex.org/W2108280101","https://openalex.org/W2111754130","https://openalex.org/W2124209874","https://openalex.org/W2128242038","https://openalex.org/W2149695599","https://openalex.org/W2389642347","https://openalex.org/W2752130168","https://openalex.org/W2767544505","https://openalex.org/W2784072063","https://openalex.org/W2815764461","https://openalex.org/W2891902476","https://openalex.org/W2922404985","https://openalex.org/W2963530915","https://openalex.org/W2963730104","https://openalex.org/W2963874443","https://openalex.org/W2963917511","https://openalex.org/W3004814728","https://openalex.org/W3102853179","https://openalex.org/W3106305005","https://openalex.org/W3163344689","https://openalex.org/W3197375668"],"related_works":["https://openalex.org/W2981445280","https://openalex.org/W2786742033","https://openalex.org/W3092754438","https://openalex.org/W3099260321","https://openalex.org/W2971642660","https://openalex.org/W1582641797","https://openalex.org/W3034945862","https://openalex.org/W2232379592","https://openalex.org/W2568364429","https://openalex.org/W2782271697","https://openalex.org/W2740833984","https://openalex.org/W3202011491","https://openalex.org/W3103307487","https://openalex.org/W1984062978","https://openalex.org/W3028787943","https://openalex.org/W3102405543","https://openalex.org/W3098033226","https://openalex.org/W3004814728","https://openalex.org/W3099496226","https://openalex.org/W1544563026"],"abstract_inverted_index":{"Graph-limit":[0],"theory":[1,146],"focuses":[2],"on":[3,33,63,87,91,96,124],"the":[4,11,28,48,64,76,111,115,125,131,136,144,151,155,158],"convergence":[5],"of":[6,8,13,24,30,51,79,94,138,147,154],"sequences":[7],"graphs":[9,25],"when":[10],"number":[12],"nodes":[14],"becomes":[15],"arbitrarily":[16],"large.":[17],"This":[18],"framework":[19],"defines":[20],"a":[21,59,82],"continuous":[22,104],"version":[23],"allowing":[26],"for":[27,85],"study":[29],"dynamical":[31],"systems":[32],"very":[34],"large":[35],"graphs,":[36],"where":[37],"classical":[38],"methods":[39],"would":[40],"become":[41],"computationally":[42],"intractable.":[43],"Through":[44],"an":[45],"approximation":[46],"procedure,":[47],"standard":[49],"system":[50],"coupled":[52],"ordinary":[53],"differential":[54],"equations":[55],"is":[56],"replaced":[57],"by":[58],"nonlocal":[60],"evolution":[61],"equation":[62],"unit":[65],"interval.":[66],"In":[67],"this":[68,72],"work,":[69],"we":[70,142],"adopt":[71],"methodology":[73],"to":[74,130,149],"explore":[75],"continuum":[77,159],"limit":[78],"random":[80],"walks,":[81],"popular":[83],"model":[84],"diffusion":[86],"graphs.":[88],"We":[89,118],"focus":[90],"two":[92],"classes":[93],"processes":[95],"dense":[97],"weighted":[98],"graph,":[99],"in":[100,103,110,157],"discrete":[101,126],"and":[102,114],"time,":[105],"whose":[106],"dynamics":[107],"are":[108],"encoded":[109],"transition":[112],"matrix":[113],"random-walk":[116],"Laplacian.":[117],"also":[119],"show":[120],"that":[121],"previous":[122],"works":[123],"heat":[127],"equation,":[128],"associated":[129],"combinatorial":[132],"Laplacian,":[133],"fall":[134],"within":[135],"scope":[137],"our":[139],"approach.":[140],"Finally,":[141],"apply":[143],"spectral":[145],"operators":[148],"characterize":[150],"relaxation":[152],"time":[153],"process":[156],"limit.":[160]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
