{"id":"https://openalex.org/W2976645955","doi":"https://doi.org/10.1007/s10208-019-09436-w","title":"Error Estimates for Spectral Convergence of the Graph Laplacian on Random Geometric Graphs Toward the Laplace\u2013Beltrami Operator","display_name":"Error Estimates for Spectral Convergence of the Graph Laplacian on Random Geometric Graphs Toward the Laplace\u2013Beltrami Operator","publication_year":2019,"publication_date":"2019-09-24","ids":{"openalex":"https://openalex.org/W2976645955","doi":"https://doi.org/10.1007/s10208-019-09436-w","mag":"2976645955"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-019-09436-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-019-09436-w","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058626346","display_name":"Nicol\u00e1s Garc\u00eda Trillos","orcid":"https://orcid.org/0000-0002-7711-5901"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nicol\u00e1s Garc\u00eda Trillos","raw_affiliation_strings":["Department of Statistics, University of Wisconsin-Madison, Madison, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Wisconsin-Madison, Madison, USA","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079236248","display_name":"Moritz Gerlach","orcid":null},"institutions":[{"id":"https://openalex.org/I91712215","display_name":"Saarland University","ror":"https://ror.org/01jdpyv68","country_code":"DE","type":"education","lineage":["https://openalex.org/I91712215"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Moritz Gerlach","raw_affiliation_strings":["Department of Mathematics and Computer Science, Saarland University, Saarbr\u00fccken, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Saarland University, Saarbr\u00fccken, Germany","institution_ids":["https://openalex.org/I91712215"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025830560","display_name":"Matthias Hein","orcid":"https://orcid.org/0000-0002-8751-7760"},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Matthias Hein","raw_affiliation_strings":["Department of Computer Science, University of T\u00fcbingen, T\u00fcbingen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of T\u00fcbingen, T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004682327","display_name":"Dejan Slep\u010dev","orcid":"https://orcid.org/0000-0002-7600-1144"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Dejan Slep\u010dev","raw_affiliation_strings":["Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USA","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5004682327"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":16.7979,"has_fulltext":false,"cited_by_count":136,"citation_normalized_percentile":{"value":0.99412981,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"20","issue":"4","first_page":"827","last_page":"887"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9839000105857849,"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/T12351","display_name":"Geometry and complex manifolds","score":0.9815999865531921,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8346642255783081},{"id":"https://openalex.org/keywords/submanifold","display_name":"Submanifold","score":0.7029755115509033},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.6622879505157471},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.6416019797325134},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5924572944641113},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.587946355342865},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5277077555656433},{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.527431309223175},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5222719311714172},{"id":"https://openalex.org/keywords/algebraic-connectivity","display_name":"Algebraic connectivity","score":0.5161195993423462},{"id":"https://openalex.org/keywords/laplace\u2013beltrami-operator","display_name":"Laplace\u2013Beltrami operator","score":0.48651331663131714},{"id":"https://openalex.org/keywords/random-geometric-graph","display_name":"Random geometric graph","score":0.48052510619163513},{"id":"https://openalex.org/keywords/spectral-graph-theory","display_name":"Spectral graph theory","score":0.4687493145465851},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3763994872570038},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3698672652244568},{"id":"https://openalex.org/keywords/p-laplacian","display_name":"p-Laplacian","score":0.3128261864185333},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.14712217450141907},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.12599226832389832},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07368248701095581}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8346642255783081},{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.7029755115509033},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.6622879505157471},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.6416019797325134},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5924572944641113},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.587946355342865},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5277077555656433},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.527431309223175},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5222719311714172},{"id":"https://openalex.org/C7948225","wikidata":"https://www.wikidata.org/wiki/Q4723998","display_name":"Algebraic connectivity","level":4,"score":0.5161195993423462},{"id":"https://openalex.org/C49747540","wikidata":"https://www.wikidata.org/wiki/Q1071846","display_name":"Laplace\u2013Beltrami operator","level":4,"score":0.48651331663131714},{"id":"https://openalex.org/C30609935","wikidata":"https://www.wikidata.org/wiki/Q7291969","display_name":"Random geometric graph","level":5,"score":0.48052510619163513},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.4687493145465851},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3763994872570038},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3698672652244568},{"id":"https://openalex.org/C203269682","wikidata":"https://www.wikidata.org/wiki/Q7116898","display_name":"p-Laplacian","level":3,"score":0.3128261864185333},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.14712217450141907},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.12599226832389832},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07368248701095581},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"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/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10208-019-09436-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10208-019-09436-w","pdf_url":null,"source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.4699999988079071,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W586055246","https://openalex.org/W630423399","https://openalex.org/W1481933820","https://openalex.org/W1493594095","https://openalex.org/W1500992145","https://openalex.org/W1563644419","https://openalex.org/W1567771969","https://openalex.org/W1572115049","https://openalex.org/W1853432610","https://openalex.org/W1974879594","https://openalex.org/W1976755703","https://openalex.org/W1984032850","https://openalex.org/W1989368986","https://openalex.org/W2002276939","https://openalex.org/W2094204876","https://openalex.org/W2097308346","https://openalex.org/W2108280101","https://openalex.org/W2132914434","https://openalex.org/W2133485974","https://openalex.org/W2143420533","https://openalex.org/W2146508075","https://openalex.org/W2157878484","https://openalex.org/W2163581538","https://openalex.org/W2610893972","https://openalex.org/W2963111412","https://openalex.org/W2963388623","https://openalex.org/W2963954124","https://openalex.org/W2964203384","https://openalex.org/W2978329087","https://openalex.org/W3100568746","https://openalex.org/W4206033904","https://openalex.org/W4213367101","https://openalex.org/W6601241631","https://openalex.org/W6606271560","https://openalex.org/W6609160193","https://openalex.org/W6610310711","https://openalex.org/W6722859720"],"related_works":["https://openalex.org/W2478475484","https://openalex.org/W4386468271","https://openalex.org/W1002309053","https://openalex.org/W2475700395","https://openalex.org/W2165755074","https://openalex.org/W2531476721","https://openalex.org/W2886117955","https://openalex.org/W2078972972","https://openalex.org/W156426934","https://openalex.org/W2161131771"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":7},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":13},{"year":2021,"cited_by_count":34},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":12},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-25T08:17:42.794288","created_date":"2025-10-10T00:00:00"}