{"id":"https://openalex.org/W3166764333","doi":"https://doi.org/10.1145/3406325.3451094","title":"Sampling matrices from Harish-Chandra\u2013Itzykson\u2013Zuber densities with applications to Quantum inference and differential privacy","display_name":"Sampling matrices from Harish-Chandra\u2013Itzykson\u2013Zuber densities with applications to Quantum inference and differential privacy","publication_year":2021,"publication_date":"2021-06-15","ids":{"openalex":"https://openalex.org/W3166764333","doi":"https://doi.org/10.1145/3406325.3451094","mag":"3166764333"},"language":"en","primary_location":{"id":"doi:10.1145/3406325.3451094","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451094","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-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/A5051294838","display_name":"Jonathan Leake","orcid":null},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Jonathan Leake","raw_affiliation_strings":["TU Berlin, Germany"],"affiliations":[{"raw_affiliation_string":"TU Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013525681","display_name":"Colin McSwiggen","orcid":"https://orcid.org/0000-0002-1960-5769"},"institutions":[{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Colin McSwiggen","raw_affiliation_strings":["University of Tokyo, Japan"],"affiliations":[{"raw_affiliation_string":"University of Tokyo, Japan","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063089732","display_name":"Nisheeth K. Vishnoi","orcid":"https://orcid.org/0000-0002-0255-1119"},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nisheeth K. Vishnoi","raw_affiliation_strings":["Yale University, USA"],"affiliations":[{"raw_affiliation_string":"Yale University, USA","institution_ids":["https://openalex.org/I32971472"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051294838"],"corresponding_institution_ids":["https://openalex.org/I4577782"],"apc_list":null,"apc_paid":null,"fwci":1.6555,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.85279705,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"1384","last_page":"1397"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9995999932289124,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9958000183105469,"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/unitary-matrix","display_name":"Unitary matrix","score":0.7146739363670349},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.6575800776481628},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.6006358861923218},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5442425012588501},{"id":"https://openalex.org/keywords/haar-measure","display_name":"Haar measure","score":0.5387054681777954},{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.4819795489311218},{"id":"https://openalex.org/keywords/circular-ensemble","display_name":"Circular ensemble","score":0.4226382076740265},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3646863102912903},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3323889374732971},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2703157961368561},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23920461535453796},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.17321786284446716}],"concepts":[{"id":"https://openalex.org/C96214315","wikidata":"https://www.wikidata.org/wiki/Q727103","display_name":"Unitary matrix","level":3,"score":0.7146739363670349},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.6575800776481628},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.6006358861923218},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5442425012588501},{"id":"https://openalex.org/C130805567","wikidata":"https://www.wikidata.org/wiki/Q1162676","display_name":"Haar measure","level":2,"score":0.5387054681777954},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.4819795489311218},{"id":"https://openalex.org/C11902944","wikidata":"https://www.wikidata.org/wiki/Q5121662","display_name":"Circular ensemble","level":4,"score":0.4226382076740265},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3646863102912903},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3323889374732971},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2703157961368561},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23920461535453796},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.17321786284446716},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3406325.3451094","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451094","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6181384838","display_name":null,"funder_award_id":"JPMJCR18T6","funder_id":"https://openalex.org/F4320334789","funder_display_name":"Japan Science and Technology Agency"},{"id":"https://openalex.org/G7725451807","display_name":null,"funder_award_id":"390685689","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8578168712","display_name":null,"funder_award_id":"CCF-1908347, DMS-1714187","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334789","display_name":"Japan Science and Technology Agency","ror":"https://ror.org/00097mb19"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W8105021","https://openalex.org/W1480800941","https://openalex.org/W1982402793","https://openalex.org/W1984800067","https://openalex.org/W1992926795","https://openalex.org/W1996999318","https://openalex.org/W2009414856","https://openalex.org/W2020464444","https://openalex.org/W2032558547","https://openalex.org/W2037528737","https://openalex.org/W2064496710","https://openalex.org/W2067514827","https://openalex.org/W2072403451","https://openalex.org/W2123820077","https://openalex.org/W2129987720","https://openalex.org/W2136189972","https://openalex.org/W2147487384","https://openalex.org/W2159921855","https://openalex.org/W2160955670","https://openalex.org/W2162461309","https://openalex.org/W2165878358","https://openalex.org/W2331762649","https://openalex.org/W2401095126","https://openalex.org/W2963765954","https://openalex.org/W3035199464","https://openalex.org/W3100881619","https://openalex.org/W3101136783","https://openalex.org/W3101297073","https://openalex.org/W3111890340","https://openalex.org/W3157797457","https://openalex.org/W4252028749"],"related_works":["https://openalex.org/W2034442087","https://openalex.org/W2072321776","https://openalex.org/W2090846666","https://openalex.org/W27990313","https://openalex.org/W1514807313","https://openalex.org/W2189398608","https://openalex.org/W3101394377","https://openalex.org/W2184469044","https://openalex.org/W3099635995","https://openalex.org/W2342178627"],"abstract_inverted_index":{"Given":[0],"two":[1,63],"Hermitian":[2],"matrices":[3,31,67],"Y":[4],"and":[5,45,88,171],"\u039b,":[6],"the":[7,14,22,26,35,50,74,89,116,163],"Harish-Chandra\u2013Itzykson\u2013Zuber":[8],"(HCIZ)":[9],"distribution":[10,37,57],"is":[11],"given":[12,168],"by":[13],"density":[15,169],"eTr(U":[16],"\u039b":[17],"U*Y)":[18],"with":[19,109,183],"respect":[20],"to":[21,34,65,73,123,139,156],"Haar":[23],"measure":[24],"on":[25,96],"unitary":[27,30,147],"group.":[28],"Random":[29],"distributed":[32],"according":[33],"HCIZ":[36,75],"are":[38,71,82,103],"important":[39],"in":[40,43,84,105,133,150],"various":[41],"settings":[42],"physics":[44],"random":[46],"matrix":[47,129],"theory,":[48],"but":[49,108],"problem":[51],"of":[52,91,128],"sampling":[53],"efficiently":[54],"from":[55,68,125,141,162],"this":[56],"has":[58],"remained":[59],"open.":[60],"We":[61],"present":[62],"algorithms":[64],"sample":[66,124,140,157],"distributions":[69,131,145],"that":[70,81,102,181],"close":[72],"distribution.":[76],"The":[77,98],"first":[78],"produces":[79,100],"samples":[80,101],"\u03be-close":[83,104],"total":[85],"variation":[86],"distance,":[87],"number":[90],"arithmetic":[92],"operations":[93],"required":[94],"depends":[95],"poly(log1/\u03be).":[97],"second":[99],"infinity":[106],"divergence,":[107],"a":[110,158,167],"poly(1/\u03be)":[111],"dependence.":[112],"Our":[113],"results":[114],"have":[115],"following":[117],"applications:":[118],"1)":[119],"an":[120,136,153,173],"efficient":[121,137,154,174],"algorithm":[122,138,155,175],"complex":[126],"versions":[127],"Langevin":[130],"studied":[132],"statistics,":[134],"2)":[135],"continuous":[142],"maximum":[143],"entropy":[144],"over":[146],"orbits,":[148],"which":[149],"turn":[151],"implies":[152],"pure":[159],"quantum":[160],"state":[161],"entropy-maximizing":[164],"ensemble":[165],"representing":[166],"matrix,":[170],"3)":[172],"for":[176,187],"differentially":[177],"private":[178],"rank-k":[179],"approximation":[180],"comes":[182],"improved":[184],"utility":[185],"bounds":[186],"k>1.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2025-10-10T00:00:00"}
