{"id":"https://openalex.org/W23504064","doi":"https://doi.org/10.48550/arxiv.0705.3600","title":"Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models","display_name":"Weil-Petersson volume of moduli spaces, Mirzakhani's recursion and matrix models","publication_year":2007,"publication_date":"2007-05-24","ids":{"openalex":"https://openalex.org/W23504064","doi":"https://doi.org/10.48550/arxiv.0705.3600","mag":"23504064"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:0705.3600","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0705.3600","pdf_url":"https://arxiv.org/pdf/0705.3600","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/0705.3600","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102851120","display_name":"Bertrand Eynard","orcid":"https://orcid.org/0000-0003-0974-4420","observed_orcids":["https://orcid.org/0000-0003-0974-4420"]},"institutions":[{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I2801360556","display_name":"CEA Paris-Saclay - Etablissement de Saclay","ror":"https://ror.org/01fv25t22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I2801360556","https://openalex.org/I4210128565"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Eynard, Bertrand","raw_affiliation_strings":["SPhT","SPhT - Service de Physique Th\u00e9orique (CEA/Saclay - 91191 Gif-sur-Yvette Cedex, France - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SPhT","institution_ids":[]},{"raw_affiliation_string":"SPhT - Service de Physique Th\u00e9orique (CEA/Saclay - 91191 Gif-sur-Yvette Cedex, France - France)","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I2801360556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000035564","display_name":"Nicolas Orantin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I2801360556","display_name":"CEA Paris-Saclay - Etablissement de Saclay","ror":"https://ror.org/01fv25t22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I2801360556","https://openalex.org/I4210128565"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Orantin, Nicolas","raw_affiliation_strings":["SPhT","SPhT - Service de Physique Th\u00e9orique (CEA/Saclay - 91191 Gif-sur-Yvette Cedex, France - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"SPhT","institution_ids":[]},{"raw_affiliation_string":"SPhT - Service de Physique Th\u00e9orique (CEA/Saclay - 91191 Gif-sur-Yvette Cedex, France - France)","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I2801360556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":182,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.37299999594688416,"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/T10304","display_name":"Geometric and Algebraic Topology","score":0.37299999594688416,"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/T11716","display_name":"Random Matrices and Applications","score":0.15199999511241913,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.1460999995470047,"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/weil-petersson-volume","display_name":"Weil-Petersson volume","score":0.9879999756813049},{"id":"https://openalex.org/keywords/moduli-space-of-riemann-surfaces","display_name":"moduli space of Riemann surfaces","score":0.9819999933242798},{"id":"https://openalex.org/keywords/matrix-models","display_name":"matrix models","score":0.8579999804496765}],"concepts":[{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.7629266977310181},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5514833927154541},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5510299801826477},{"id":"https://openalex.org/C73373263","wikidata":"https://www.wikidata.org/wiki/Q845677","display_name":"Moduli space","level":2,"score":0.5467946529388428},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.5448458790779114},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5346813201904297},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.48790618777275085},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21948924660682678},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.09111574292182922},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.07720926403999329},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.052407801151275635},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.04389774799346924},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:0705.3600","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0705.3600","pdf_url":"https://arxiv.org/pdf/0705.3600","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":"pmh:oai:HAL:hal-00149179v1","doi":null,"is_oa":true,"landing_page_url":"https://hal.science/hal-00149179","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I4405252976","host_organization_name":"Centre pour la Communication Scientifique Directe","host_organization_lineage":["https://openalex.org/I4405252976"],"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":"2007","raw_type":"info:eu-repo/semantics/preprint"},{"id":"doi:10.48550/arxiv.0705.3600","doi":"https://doi.org/10.48550/arxiv.0705.3600","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.0705.3600","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:0705.3600","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/0705.3600","pdf_url":"https://arxiv.org/pdf/0705.3600","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":[{"id":"https://openalex.org/F4320320301","display_name":"European Science Foundation","ror":"https://ror.org/04esata81"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321747","display_name":"Fonds Qu\u00e9b\u00e9cois de la Recherche sur la Nature et les Technologies","ror":"https://ror.org/00b9f9778"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W23504064.pdf","grobid_xml":"https://content.openalex.org/works/W23504064.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W1524762130","https://openalex.org/W1877128492","https://openalex.org/W1986699862","https://openalex.org/W2006442667"],"related_works":["https://openalex.org/W7098412017","https://openalex.org/W1977218731","https://openalex.org/W7099814079","https://openalex.org/W4246323109","https://openalex.org/W7097633664","https://openalex.org/W1901254392","https://openalex.org/W3099700518","https://openalex.org/W4323651246","https://openalex.org/W7135242495","https://openalex.org/W2609595815"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,28],"Mirzakhani's":[3],"recursions":[4],"for":[5,35,45],"the":[6,46],"volumes":[7],"of":[8,11,18],"moduli":[9],"space":[10],"Riemann":[12],"surfaces":[13],"are":[14],"a":[15,32,43],"special":[16],"case":[17],"random":[19],"matrix":[20],"loop":[21],"equations,":[22],"and":[23],"therefore":[24],"we":[25,41],"confirm":[26],"again":[27],"Kontsevitch's":[29],"integral":[30],"is":[31],"generating":[33],"function":[34],"those":[36],"volumes.":[37],"As":[38],"an":[39],"application,":[40],"propose":[42],"formula":[44],"Weil-Petersson":[47],"volume":[48],"Vol(M_{g,0}).":[49]},"counts_by_year":[{"year":2026,"cited_by_count":27},{"year":2025,"cited_by_count":19},{"year":2024,"cited_by_count":16},{"year":2023,"cited_by_count":17},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":14},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":6}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}
