{"id":"https://openalex.org/W7220971231","doi":"https://doi.org/10.48550/arxiv.2610.10501","title":"The Tutte embedding of tree-weighted planar maps converges to Liouville quantum gravity","display_name":"The Tutte embedding of tree-weighted planar maps converges to Liouville quantum gravity","publication_year":2026,"publication_date":"2026-10-07","ids":{"openalex":"https://openalex.org/W7220971231","doi":"https://doi.org/10.48550/arxiv.2610.10501"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.10501","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10501","pdf_url":"https://arxiv.org/pdf/2610.10501","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/2610.10501","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034106138","display_name":"Nina Holden","orcid":"https://orcid.org/0000-0001-9259-4704","observed_orcids":["https://orcid.org/0000-0001-9259-4704"]},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]},{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Holden, Nina","raw_affiliation_strings":["Courant Institute , New York University ;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Courant Institute , New York University ;","institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034106138"],"corresponding_institution_ids":["https://openalex.org/I36672615","https://openalex.org/I57206974"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9887999892234802,"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"}},"topics":[{"id":"https://openalex.org/T11152","display_name":"Stochastic processes and statistical mechanics","score":0.9887999892234802,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.006099999882280827,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T13234","display_name":"p-Adic Analysis and Mathematical Physics","score":0.0008999999845400453,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/planar-maps","display_name":"planar maps","score":0.8799999952316284},{"id":"https://openalex.org/keywords/liouville-quantum-gravity","display_name":"Liouville quantum gravity","score":0.8999999761581421},{"id":"https://openalex.org/keywords/spanning-trees","display_name":"spanning trees","score":0.8019999861717224},{"id":"https://openalex.org/keywords/planar-brownian-motion","display_name":"planar Brownian motion","score":0.9350000023841858}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6859999895095825},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.66839998960495},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6639999747276306},{"id":"https://openalex.org/C112401455","wikidata":"https://www.wikidata.org/wiki/Q178036","display_name":"Brownian motion","level":2,"score":0.5982000231742859},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4837999939918518},{"id":"https://openalex.org/C108568745","wikidata":"https://www.wikidata.org/wiki/Q234181","display_name":"Quantum gravity","level":3,"score":0.44429999589920044},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.44339999556541443},{"id":"https://openalex.org/C121194460","wikidata":"https://www.wikidata.org/wiki/Q856741","display_name":"Random walk","level":2,"score":0.4392000138759613},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.400299996137619},{"id":"https://openalex.org/C140058369","wikidata":"https://www.wikidata.org/wiki/Q7269113","display_name":"Quantum walk","level":4,"score":0.36739999055862427},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3659000098705292},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.34940001368522644},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C64331007","wikidata":"https://www.wikidata.org/wiki/Q831672","display_name":"Spanning tree","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29510000348091125},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.2939999997615814},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2800999879837036},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.274399995803833},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.27059999108314514},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C187619975","wikidata":"https://www.wikidata.org/wiki/Q848427","display_name":"Julia set","level":2,"score":0.26660001277923584},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.25609999895095825},{"id":"https://openalex.org/C2776839635","wikidata":"https://www.wikidata.org/wiki/Q14942679","display_name":"Random tree","level":4,"score":0.25380000472068787}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.10501","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10501","pdf_url":"https://arxiv.org/pdf/2610.10501","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":"doi:10.48550/arxiv.2610.10501","doi":"https://doi.org/10.48550/arxiv.2610.10501","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.10501","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:2610.10501","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.10501","pdf_url":"https://arxiv.org/pdf/2610.10501","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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220971231.pdf","grobid_xml":"https://content.openalex.org/works/W7220971231.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2619961998","https://openalex.org/W7220992121","https://openalex.org/W4410525942","https://openalex.org/W2892229510","https://openalex.org/W6925254098","https://openalex.org/W3012710623","https://openalex.org/W2979974011","https://openalex.org/W6962895536","https://openalex.org/W2775376271","https://openalex.org/W7095624280"],"abstract_inverted_index":{"Suppose":[0],"$M$":[1,30,52,65],"is":[2],"a":[3,7,12,33,68],"planar":[4,69],"map":[5],"with":[6,38],"macroscopic":[8],"boundary":[9,50],"decorated":[10],"by":[11],"spanning":[13],"tree":[14],"$T$,":[15],"such":[16],"that":[17,29],"$(M,T)$":[18],"has":[19],"been":[20],"sampled":[21],"from":[22],"the":[23,42,46,49,60],"critical":[24],"Boltzman":[25],"measure.":[26],"We":[27],"show":[28],"converges":[31,66],"to":[32,54,67],"Liouville":[34],"quantum":[35],"gravity":[36],"disk":[37],"parameter":[39],"$\u03b3=\\sqrt{2}$":[40],"under":[41],"Tutte":[43],"embedding":[44],"as":[45],"length":[47],"of":[48,51,74],"goes":[53],"infinity.":[55],"Furthermore,":[56],"conditioned":[57],"on":[58,64],"$(M,T)$,":[59],"simple":[61],"random":[62],"walk":[63],"Brownian":[70],"motion":[71],"modulo":[72],"reparametrization":[73],"time.":[75]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-09T00:00:00"}