{"id":"https://openalex.org/W3034629269","doi":"https://doi.org/10.1109/lcsys.2020.3009035","title":"On the Influence of Noise in Randomized Consensus Algorithms","display_name":"On the Influence of Noise in Randomized Consensus Algorithms","publication_year":2020,"publication_date":"2020-07-13","ids":{"openalex":"https://openalex.org/W3034629269","doi":"https://doi.org/10.1109/lcsys.2020.3009035","mag":"3034629269"},"language":"en","primary_location":{"id":"doi:10.1109/lcsys.2020.3009035","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2020.3009035","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Control Systems Letters","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2006.05753","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069126376","display_name":"Renato Vizuete","orcid":"https://orcid.org/0000-0001-7820-2217"},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210101348","display_name":"Centre Inria de l'Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/00n8d6z93","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210101348"]},{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I4210124956","display_name":"GIPSA-Lab","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Renato Vizuete","raw_affiliation_strings":["CNRS, CentraleSup\u00e9lec, Laboratoire des signaux et syst\u00e8mes, Universit\u00e9 Paris-Saclay, Gif-sur-Yvette, France","CNRS, Inria, Grenoble INP, GIPSA-lab, University Grenoble Alpes, Grenoble, France","[CNRS, CentraleSupelec, Laboratoire des Signaux et Syst\u00e8mes, Universit\u00e9 Paris-Saclay, Gif-sur-Yvette, France]"],"raw_orcid":"https://orcid.org/0000-0001-7820-2217","affiliations":[{"raw_affiliation_string":"CNRS, CentraleSup\u00e9lec, Laboratoire des signaux et syst\u00e8mes, Universit\u00e9 Paris-Saclay, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210107720"]},{"raw_affiliation_string":"CNRS, Inria, Grenoble INP, GIPSA-lab, University Grenoble Alpes, Grenoble, France","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210101348","https://openalex.org/I4210124956","https://openalex.org/I899635006"]},{"raw_affiliation_string":"[CNRS, CentraleSupelec, Laboratoire des Signaux et Syst\u00e8mes, Universit\u00e9 Paris-Saclay, Gif-sur-Yvette, France]","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210107720"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050626793","display_name":"Paolo Frasca","orcid":"https://orcid.org/0000-0003-0962-3119"},"institutions":[{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210101348","display_name":"Centre Inria de l'Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/00n8d6z93","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210101348"]},{"id":"https://openalex.org/I4210124956","display_name":"GIPSA-Lab","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Paolo Frasca","raw_affiliation_strings":["CNRS, Inria, Grenoble INP, GIPSA-lab, University Grenoble Alpes, Grenoble, France","[CNRS, Inria, Grenoble INP, GIPSA-Lab, Univ. Grenoble Alpes, Grenoble, France]"],"raw_orcid":"https://orcid.org/0000-0003-0962-3119","affiliations":[{"raw_affiliation_string":"CNRS, Inria, Grenoble INP, GIPSA-lab, University Grenoble Alpes, Grenoble, France","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210101348","https://openalex.org/I4210124956","https://openalex.org/I899635006"]},{"raw_affiliation_string":"[CNRS, Inria, Grenoble INP, GIPSA-Lab, Univ. Grenoble Alpes, Grenoble, France]","institution_ids":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210101348","https://openalex.org/I4210124956","https://openalex.org/I899635006"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036042991","display_name":"Elena Panteley","orcid":"https://orcid.org/0000-0002-4565-9138"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I277688954","display_name":"Universit\u00e9 Paris-Saclay","ror":"https://ror.org/03xjwb503","country_code":"FR","type":"education","lineage":["https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Elena Panteley","raw_affiliation_strings":["CNRS, CentraleSup\u00e9lec, Laboratoire des signaux et syst\u00e8mes, Universit\u00e9 Paris-Saclay, Gif-sur-Yvette, France","[CNRS, CentraleSupelec, Laboratoire des Signaux et Syst\u00e8mes, Universit\u00e9 Paris-Saclay, Gif-sur-Yvette, France]"],"raw_orcid":"https://orcid.org/0000-0002-4565-9138","affiliations":[{"raw_affiliation_string":"CNRS, CentraleSup\u00e9lec, Laboratoire des signaux et syst\u00e8mes, Universit\u00e9 Paris-Saclay, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210107720"]},{"raw_affiliation_string":"[CNRS, CentraleSupelec, Laboratoire des Signaux et Syst\u00e8mes, Universit\u00e9 Paris-Saclay, Gif-sur-Yvette, France]","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I4210107720"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09703932,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"3","first_page":"1025","last_page":"1030"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12592","display_name":"Opinion Dynamics and Social Influence","score":0.9966999888420105,"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"}},{"id":"https://openalex.org/T10064","display_name":"Complex Network Analysis Techniques","score":0.9890000224113464,"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/laplacian-matrix","display_name":"Laplacian matrix","score":0.704544186592102},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6056760549545288},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5906173586845398},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5742320418357849},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5316911935806274},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4900625944137573},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4822891056537628},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.4786564111709595},{"id":"https://openalex.org/keywords/randomized-algorithm","display_name":"Randomized algorithm","score":0.4499798119068146},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41810375452041626},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.41419756412506104},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39215588569641113},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2995344400405884},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11897960305213928},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09464564919471741}],"concepts":[{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.704544186592102},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6056760549545288},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5906173586845398},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5742320418357849},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5316911935806274},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4900625944137573},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4822891056537628},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.4786564111709595},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.4499798119068146},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41810375452041626},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.41419756412506104},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39215588569641113},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2995344400405884},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11897960305213928},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09464564919471741},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/lcsys.2020.3009035","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2020.3009035","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Control Systems Letters","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2006.05753","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.05753","pdf_url":"https://arxiv.org/pdf/2006.05753","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":null},{"id":"mag:3034629269","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2006.05753v1","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:HAL:hal-02899936v1","is_oa":true,"landing_page_url":"https://centralesupelec.hal.science/hal-02899936","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Control Systems Letters, 2021, 5 (3), pp.1025-1030. &#x27E8;10.1109/LCSYS.2020.3009035&#x27E9;","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2006.05753","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2006.05753","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2006.05753","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2006.05753","pdf_url":"https://arxiv.org/pdf/2006.05753","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":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2127059016","display_name":"Hybrid And Networked Dynamical sYstems","funder_award_id":"ANR-18-CE40-0010","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G4724914523","display_name":null,"funder_award_id":"HANDY ANR-18-CE40-0010","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1533442304","https://openalex.org/W2005446274","https://openalex.org/W2033895804","https://openalex.org/W2073734023","https://openalex.org/W2073859315","https://openalex.org/W2081542735","https://openalex.org/W2081632029","https://openalex.org/W2129248505","https://openalex.org/W2134252677","https://openalex.org/W2138624490","https://openalex.org/W2145706050","https://openalex.org/W2151685478","https://openalex.org/W2160413708","https://openalex.org/W2588797492","https://openalex.org/W2762146562","https://openalex.org/W2803648438","https://openalex.org/W2913323902","https://openalex.org/W2963567876","https://openalex.org/W2963984324","https://openalex.org/W3012540517"],"related_works":["https://openalex.org/W2954158457","https://openalex.org/W2509152809","https://openalex.org/W2295109284","https://openalex.org/W1489437880","https://openalex.org/W2290956892","https://openalex.org/W2890444536","https://openalex.org/W2950114483","https://openalex.org/W2780298283","https://openalex.org/W2972071922","https://openalex.org/W2885478882","https://openalex.org/W2147129668","https://openalex.org/W2791138598","https://openalex.org/W2890261666","https://openalex.org/W857387926","https://openalex.org/W1973271179","https://openalex.org/W2938493800","https://openalex.org/W2074022433","https://openalex.org/W2963556049","https://openalex.org/W2938670946","https://openalex.org/W3035946839"],"abstract_inverted_index":{"In":[0],"this":[1],"letter,":[2],"we":[3,21,55,81,108],"study":[4,50],"the":[5,16,28,34,49,83,87,90,94,98,112],"influence":[6],"of":[7,51,64,73,89,93,117],"additive":[8],"noise":[9],"in":[10],"randomized":[11],"consensus":[12],"algorithms.":[13],"Assuming":[14],"that":[15,42,67],"update":[17,65],"matrices":[18,66],"are":[19,43,68],"symmetric,":[20],"derive":[22,109],"a":[23,62,74],"closed":[24],"form":[25],"expression":[26],"for":[27,111],"mean":[29],"square":[30],"error":[31],"induced":[32],"by":[33,48,70,85],"noise,":[35],"together":[36],"with":[37],"upper":[38],"and":[39,119],"lower":[40],"bounds":[41,84,113],"simpler":[44],"to":[45],"evaluate.":[46],"Motivated":[47],"Open":[52],"Multi-Agent":[53],"Systems,":[54],"concentrate":[56],"on":[57,114],"Randomly":[58],"Induced":[59],"Discretized":[60],"Laplacians,":[61],"family":[63],"generated":[69],"sampling":[71],"subgraphs":[72],"large":[75],"undirected":[76],"graph.":[77],"For":[78],"these":[79],"matrices,":[80],"express":[82],"using":[86],"eigenvalues":[88],"Laplacian":[91],"matrix":[92],"underlying":[95],"graph":[96],"or":[97],"graph's":[99],"average":[100],"effective":[101],"resistance,":[102],"thereby":[103],"proving":[104],"their":[105],"tightness.":[106],"Finally,":[107],"expressions":[110],"some":[115],"examples":[116],"graphs":[118],"numerically":[120],"evaluate":[121],"them.":[122]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
