{"id":"https://openalex.org/W874374694","doi":null,"title":"Combinatorics Of The Hermitian One-Matrix Model","display_name":"Combinatorics Of The Hermitian One-Matrix Model","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W874374694","mag":"874374694"},"language":"en","primary_location":{"id":"pmh:oai:repository.arizona.edu:10150/556704","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/10150/556704","pdf_url":null,"source":{"id":"https://openalex.org/S4306400271","display_name":"UA Campus Repository (The University of Arizona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I138006243","host_organization_name":"University of Arizona","host_organization_lineage":["https://openalex.org/I138006243"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Electronic Dissertation"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"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/A5024004981","display_name":"Patrick Waters","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Patrick Waters","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5024004981"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":1,"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/T11716","display_name":"Random Matrices and Applications","score":0.9761000275611877,"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"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9761000275611877,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.007600000128149986,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.004000000189989805,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hermitian-one-matrix-model","display_name":"Hermitian one-matrix model","score":0.9440000057220459},{"id":"https://openalex.org/keywords/string-equation","display_name":"string equation","score":0.7429999709129333},{"id":"https://openalex.org/keywords/equilibrium-measure","display_name":"equilibrium measure","score":0.8740000128746033},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"orthogonal polynomials","score":0.7689999938011169},{"id":"https://openalex.org/keywords/riemann-hilbert-problem","display_name":"Riemann-Hilbert problem","score":0.9300000071525574},{"id":"https://openalex.org/keywords/loop-equations","display_name":"loop equations","score":0.9950000047683716},{"id":"https://openalex.org/keywords/polynomial-potentials","display_name":"polynomial potentials","score":0.6650000214576721},{"id":"https://openalex.org/keywords/random-matrix-theory","display_name":"random matrix theory","score":0.4050000011920929},{"id":"https://openalex.org/keywords/combinatorial-enumeration","display_name":"combinatorial enumeration","score":0.7699999809265137}],"concepts":[{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.705933690071106},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6530411243438721},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4973340332508087},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45614075660705566},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4157216548919678},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3749006688594818},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32085517048835754},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.21808922290802002},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1866600513458252},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:repository.arizona.edu:10150/556704","doi":null,"is_oa":false,"landing_page_url":"http://hdl.handle.net/10150/556704","pdf_url":null,"source":{"id":"https://openalex.org/S4306400271","display_name":"UA Campus Repository (The University of Arizona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I138006243","host_organization_name":"University of Arizona","host_organization_lineage":["https://openalex.org/I138006243"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Electronic Dissertation"},{"id":"mag:874374694","doi":null,"is_oa":false,"landing_page_url":"http://arizona.openrepository.com/arizona/handle/10150/556704","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W350097702","https://openalex.org/W610035724","https://openalex.org/W1499838523","https://openalex.org/W1524762130","https://openalex.org/W1585244820","https://openalex.org/W1590857171","https://openalex.org/W1745721203","https://openalex.org/W1765024896","https://openalex.org/W1884272320","https://openalex.org/W1966010547","https://openalex.org/W1972563066","https://openalex.org/W1977389927","https://openalex.org/W1999215941","https://openalex.org/W2000650424","https://openalex.org/W2010894431","https://openalex.org/W2012238557","https://openalex.org/W2023322777","https://openalex.org/W2029265825","https://openalex.org/W2033292040","https://openalex.org/W2034573815","https://openalex.org/W2043858660","https://openalex.org/W2044745523","https://openalex.org/W2056423564","https://openalex.org/W2059786538","https://openalex.org/W2065761068","https://openalex.org/W2076641463","https://openalex.org/W2077030884","https://openalex.org/W2088929863","https://openalex.org/W2124590498","https://openalex.org/W2137247574","https://openalex.org/W2137740584","https://openalex.org/W2139335416","https://openalex.org/W2144353909","https://openalex.org/W2160595403","https://openalex.org/W2165878358","https://openalex.org/W2288453532","https://openalex.org/W2950732721","https://openalex.org/W2963431616","https://openalex.org/W2963734224","https://openalex.org/W2964024592"],"related_works":["https://openalex.org/W1959027072","https://openalex.org/W1788708422","https://openalex.org/W2043858660","https://openalex.org/W7097735366","https://openalex.org/W2952914116","https://openalex.org/W2084472031","https://openalex.org/W4400195970","https://openalex.org/W2140828748","https://openalex.org/W7095623526","https://openalex.org/W7095959846"],"abstract_inverted_index":{"It":[0],"is":[1],"well":[2],"known":[3],"that":[4,124],"the":[5,26,90,106,112,119,137,145],"perturbed":[6],"GUE":[7],"matrix":[8,113],"model":[9],"has":[10,44],"a":[11,41,101],"combinatorial":[12],"interpretation":[13],"involving":[14],"graphs":[15,24],"embedded":[16],"in":[17,25],"Riemann":[18],"surfaces.":[19],"Generating":[20],"functions":[21,131],"for":[22,56,63,105,109,118,129,140],"these":[23],"case":[27,39,91],"of":[28,40,84,92,111],"an":[29,93],"even":[30,97],"potential":[31,43],"have":[32],"been":[33,46],"studied":[34],"by":[35],"many":[36],"authors.":[37],"The":[38],"cubic":[42],"also":[45,133],"studied.":[47],"Using":[48,115],"string":[49],"equations,":[50],"we":[51,73,122],"construct":[52],"\"valence":[53],"independent\"":[54],"formulas":[55,61,80,83,128],"map":[57],"generating":[58,130],"functions.":[59],"These":[60],"hold":[62],"arbitrary":[64,94],"polynomial":[65],"potentials.":[66],"We":[67,99],"derive":[68,100],"\"edge":[69],"Toda":[70],"equations,\"":[71],"which":[72],"use":[74],"together":[75],"with":[76],"our":[77,125],"valence":[78,102,126],"independent":[79,103,127],"to":[81,89],"generalize":[82],"Ercolani,":[85],"McLaughlin":[86],"and":[87,143],"Pierce":[88],"odd":[95],"or":[96],"valence.":[98],"formula":[104,117],"equilibrium":[107,120],"measure":[108,121],"eigenvalues":[110],"model.":[114],"this":[116],"show":[123],"can":[132],"be":[134],"derived":[135],"from":[136,144],"Riemann-Hilbert":[138],"problem":[139],"orthogonal":[141],"polynomials,":[142],"loop":[146],"equations.":[147]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}