{"id":"https://openalex.org/W157600748","doi":null,"title":"\u00c9tats al\u00e9atoires, th\u00e9orie quantique de l'information et probabilit\u00e9s libres","display_name":"\u00c9tats al\u00e9atoires, th\u00e9orie quantique de l'information et probabilit\u00e9s libres","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W157600748","mag":"157600748"},"language":"fr","primary_location":{"id":"pmh:oai:HAL:tel-00371592v1","doi":null,"is_oa":true,"landing_page_url":"https://theses.hal.science/tel-00371592v1/document","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":"Math\u00e9matiques [math]. Universit\u00e9 Claude Bernard - Lyon I, 2009. Fran\u00e7ais. ⟨NNT : ⟩","raw_type":"info:eu-repo/semantics/doctoralThesis"},"volume":null,"type":"dissertation","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://theses.hal.science/tel-00371592v1/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041561607","display_name":"Ion Nechita","orcid":"https://orcid.org/0000-0003-3016-7795","observed_orcids":["https://orcid.org/0000-0003-3016-7795"]},"institutions":[{"id":"https://openalex.org/I4210104796","display_name":"Institut Camille Jordan","ror":"https://ror.org/01ekw7f87","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I112936343","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I4210104796","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Ion Nechita","raw_affiliation_strings":["Institut Camille Jordan [Villeurbanne]"],"raw_orcid":"https://orcid.org/0000-0003-3016-7795","affiliations":[{"raw_affiliation_string":"Institut Camille Jordan [Villeurbanne]","institution_ids":["https://openalex.org/I4210104796"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5041561607"],"corresponding_institution_ids":["https://openalex.org/I4210104796"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11716","display_name":"Random Matrices and Applications","score":0.9682999849319458,"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":0.9682999849319458,"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/T10899","display_name":"Advanced Operator Algebra Research","score":0.014499999582767487,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.0035000001080334187,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/random-matrix-theory","display_name":"random matrix theory","score":0.6830000281333923},{"id":"https://openalex.org/keywords/free-probability","display_name":"free probability","score":0.9750000238418579},{"id":"https://openalex.org/keywords/quantum-information","display_name":"quantum information","score":0.7559999823570251},{"id":"https://openalex.org/keywords/quantum-catalysis","display_name":"quantum catalysis","score":0.9990000128746033},{"id":"https://openalex.org/keywords/large-deviations","display_name":"large deviations","score":0.9750000238418579},{"id":"https://openalex.org/keywords/asymptotic-freeness","display_name":"asymptotic freeness","score":0.9350000023841858},{"id":"https://openalex.org/keywords/permutations","display_name":"permutations","score":0.6740000247955322},{"id":"https://openalex.org/keywords/cycles","display_name":"cycles","score":0.4339999854564667},{"id":"https://openalex.org/keywords/symmetric-difference","display_name":"symmetric difference","score":0.4830000102519989},{"id":"https://openalex.org/keywords/free-products","display_name":"free products","score":0.6470000147819519}],"concepts":[{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.7727043628692627},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36495813727378845},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.3454284369945526}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:HAL:tel-00371592v1","doi":null,"is_oa":true,"landing_page_url":"https://theses.hal.science/tel-00371592v1/document","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":"Math\u00e9matiques [math]. Universit\u00e9 Claude Bernard - Lyon I, 2009. Fran\u00e7ais. ⟨NNT : ⟩","raw_type":"info:eu-repo/semantics/doctoralThesis"},{"id":"mag:157600748","doi":null,"is_oa":false,"landing_page_url":"http://mysite.science.uottawa.ca/inechita//talks/these_slides.pdf","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":{"id":"pmh:oai:HAL:tel-00371592v1","doi":null,"is_oa":true,"landing_page_url":"https://theses.hal.science/tel-00371592v1/document","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":"Math\u00e9matiques [math]. Universit\u00e9 Claude Bernard - Lyon I, 2009. Fran\u00e7ais. ⟨NNT : ⟩","raw_type":"info:eu-repo/semantics/doctoralThesis"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":73,"referenced_works":["https://openalex.org/W76426102","https://openalex.org/W145214010","https://openalex.org/W322525841","https://openalex.org/W1520752838","https://openalex.org/W1538087792","https://openalex.org/W1552450268","https://openalex.org/W1559181631","https://openalex.org/W1567200859","https://openalex.org/W1582318892","https://openalex.org/W1631356911","https://openalex.org/W1839260354","https://openalex.org/W1860719571","https://openalex.org/W1937644046","https://openalex.org/W1968790908","https://openalex.org/W1974998275","https://openalex.org/W1976288589","https://openalex.org/W1976625337","https://openalex.org/W1987279739","https://openalex.org/W1993932014","https://openalex.org/W1995999485","https://openalex.org/W2002429786","https://openalex.org/W2002490441","https://openalex.org/W2004353938","https://openalex.org/W2004853053","https://openalex.org/W2018340769","https://openalex.org/W2027633165","https://openalex.org/W2027976682","https://openalex.org/W2028300984","https://openalex.org/W2031566596","https://openalex.org/W2034068158","https://openalex.org/W2035501532","https://openalex.org/W2040087419","https://openalex.org/W2043865211","https://openalex.org/W2044885737","https://openalex.org/W2051302879","https://openalex.org/W2057167521","https://openalex.org/W2058846297","https://openalex.org/W2059120410","https://openalex.org/W2059619743","https://openalex.org/W2059682894","https://openalex.org/W2063211788","https://openalex.org/W2065618179","https://openalex.org/W2069719109","https://openalex.org/W2071160621","https://openalex.org/W2071937582","https://openalex.org/W2073572229","https://openalex.org/W2074505997","https://openalex.org/W2075136665","https://openalex.org/W2075405150","https://openalex.org/W2092275089","https://openalex.org/W2093399015","https://openalex.org/W2094810855","https://openalex.org/W2105318749","https://openalex.org/W2132886647","https://openalex.org/W2136118086","https://openalex.org/W2138876637","https://openalex.org/W2141140927","https://openalex.org/W2165730988","https://openalex.org/W2256588963","https://openalex.org/W2276336683","https://openalex.org/W2465087930","https://openalex.org/W2725812516","https://openalex.org/W2728821228","https://openalex.org/W2751862591","https://openalex.org/W2950427145","https://openalex.org/W3023808427","https://openalex.org/W3098548805","https://openalex.org/W3099282663","https://openalex.org/W3100793034","https://openalex.org/W3103248090","https://openalex.org/W3103503700","https://openalex.org/W3104522527","https://openalex.org/W3106202711"],"related_works":["https://openalex.org/W4392474208","https://openalex.org/W7149284527","https://openalex.org/W7143460125","https://openalex.org/W4392445230","https://openalex.org/W160180789","https://openalex.org/W7134150345","https://openalex.org/W7147517192","https://openalex.org/W7152615054","https://openalex.org/W382629287","https://openalex.org/W3036034674"],"abstract_inverted_index":{"Cette":[0,584],"th\u00e8se":[1,57,124,295,410,683],"se":[2,29,144,442,657,684],"trouve":[3,145],"\u00e0":[4,60,67,244,414,488,502,515,519,625,686],"l'intersection":[5,687],"de":[6,16,19,35,55,80,86,94,119,181,213,231,272,299,307,320,341,354,359,363,380,389,393,398,422,441,450,469,485,547,549,562,564,595,615,619,629,651,663,665,688,702],"la":[7,17,61,95,107,110,153,232,284,297,302,318,327,342,347,372,448,516,699],"th\u00e9orie":[8,18,50,62,78,96,305,343,348,373,573,700],"des":[9,12,26,43,63,97,103,127,160,173,177,192,203,219,235,258,344,349,357,361,374,426,453,467,489,503,513,541,574,612,622,627,661,671,677],"matrices":[10,44,72,87,98,104,161,178,273,407,423,454,628,693],"al\u00e9atoires,":[11,99,408,694],"probabilit\u00e9s":[13,64,345,418,530,575,696],"libres":[14,65,512,697],"et":[15,66,74,140,189,210,238,323,368,388,429,509,599,618,648,698,710],"l'information":[20,36,75,394],"quantique.":[21,51,76],"La":[22],"plus":[23],"grande":[24],"partie":[25,54],"travaux":[27,338,416,678],"pr\u00e9sent\u00e9s":[28,680],"concentrent":[30],"sur":[31,41,156,301,707,711],"les":[32,71,185,190,229,280,406,483,507,510,692,695,708,712],"aspects":[33],"probabilistes":[34],"quantique":[37,79,209,306,395,701],"et,":[38],"en":[39,49,226,242,304,403,417,465,529,532,572],"particulier,":[40],"l'usage":[42],"al\u00e9atoires":[45,73,163,179,221,275,424],"dans":[46,92,106,122,146,167,222,283,293,330,336,471,681],"diff\u00e9rents":[47,84],"mod\u00e8les":[48,85,281],"Une":[52,456],"autre":[53,386],"cette":[56,123,294,321,409,520,682],"est":[58,125,136,296,438,445,494],"d\u00e9di\u00e9e":[59],"ses":[68],"liens":[69,174,713],"avec":[70,138,175,198,279,311,371,405,452,554],"En":[77,151,171,196,309,552,604,632,674],"l'information,":[81,703],"il":[82,437],"existe":[83],"densit\u00e9s":[88,162,186,274],"al\u00e9atoires.":[89],"On":[90,253],"s'int\u00e9resse,":[91],"l'esprit":[93],"au":[100,587,659],"comportement":[101],"asymptotique":[102],"densit\u00e9s,":[105],"limite":[108],"o\u00f9":[109,131,431],"taille":[111,630],"du":[112,473,644,649],"syst\u00e8me":[113,142,208],"converge":[114],"vers":[115,317],"l'infini.":[116],"Le":[117],"point":[118],"vue":[120],"pris":[121],"celui":[126],"syst\u00e8mes":[128,214],"quantiques":[129],"ouverts,":[130],"l'espace":[132,563,594],"qui":[133,288,497,668],"nous":[134,314,324,339,352,377,498,523,557,607],"int\u00e9resse":[135],"coupl\u00e9":[137],"l'environnement":[139],"le":[141,369,534,538],"compos\u00e9":[143],"un":[147,207,261,269,385,396,526,569,578],"\u00e9tat":[148],"pur":[149],"uniforme.":[150,252],"prenant":[152],"trace":[154],"partielle":[155],"l'environnement,":[157],"on":[158,183,201,267,479],"obtient":[159,184],"que":[164,228,276],"l'on":[165,277,432],"\u00e9tudie":[166,202],"deux":[168,415],"r\u00e9gimes":[169],"asymptotiques.":[170],"exploitant":[172],"l'ensemble":[176,676],"dites":[180],"Wishart,":[182],"spectrales":[187],"limites":[188],"fluctuations":[191],"valeurs":[193],"propres":[194],"extr\u00e9males.":[195],"collaboration":[197,310,553],"Cl\u00e9ment":[199],"Pellegrini,":[200],"interactions":[204,709],"r\u00e9p\u00e9t\u00e9es":[205],"entre":[206,714],"une":[211,247,290,560,590,610],"cha\u00eene":[212,233],"auxiliaires.":[215],"Nous":[216],"avons":[217,315,524,558,608],"introduit":[218,268],"\u00e9l\u00e9ments":[220],"ce":[223,382,496],"mod\u00e8le,":[224],"soit":[225,241],"consid\u00e9rant":[227],"\u00e9tats":[230],"sont":[234,425,636],"variables":[236,514],"ind\u00e9pendantes":[237],"identiquement":[239],"distribu\u00e9es,":[240],"choisissant,":[243],"chaque":[245],"interaction,":[246],"matrice":[248],"unitaire":[249],"d'interaction":[250],"al\u00e9atoire":[251],"s'int\u00e9resse":[254],"aux":[255,391],"propri\u00e9t\u00e9s":[256],"asymptotiques":[257],"matrices,":[259],"apr\u00e8s":[260],"grand":[262],"nombre":[263],"d'interactions.":[264],"Au":[265],"passage,":[266],"nouveau":[270],"mod\u00e8le":[271,527],"compare":[278],"existants":[282],"litt\u00e9rature.":[285],"Un":[286],"probl\u00e8me":[287,383],"occupe":[289],"place":[291],"centrale":[292],"conjecture":[298,322],"Nielsen":[300],"catalyse":[303],"l'information.":[308],"Guillaume":[312],"Aubrun,":[313],"progress\u00e9":[316],"preuve":[319],"l'avons":[325],"par":[326,462,537,577,601,621],"suite":[328],"g\u00e9n\u00e9ralis\u00e9e":[329],"diff\u00e9rentes":[331],"directions.":[332],"L'outil":[333],"principal":[334],"utilis\u00e9":[335],"ces":[337,634,655,715],"vient":[340],":":[346],"grandes":[350,375,690],"d\u00e9viations":[351,376],"permet":[353],"comparer":[355],"stochastiquement":[356],"puissances":[358],"convolution":[360],"mesures":[362],"probabilit\u00e9s.":[364],"Les":[365,420],"techniques":[366],"introduites":[367],"lien":[370,404],"ont":[378],"permis":[379,500],"voir":[381],"sous":[384],"angle":[387],"donner":[390],"th\u00e9oriciens":[392],"outil":[397],"travail":[399],"puissant.":[400],"Enfin,":[401],"toujours":[402],"a":[411,459,480,499],"donn\u00e9":[412],"lieu":[413],"libres.":[419],"ensembles":[421],"exemples":[427],"importants":[428],"simples":[430],"peut":[433],"observer":[434],"l'ind\u00e9pendance":[435],"libre;":[436],"donc":[439],"naturel":[440],"demander":[443],"s'il":[444],"possible":[446],"d'obtenir":[447],"notion":[449],"libert\u00e9":[451],"d\u00e9terministes.":[455],"telle":[457],"construction":[458,591],"\u00e9t\u00e9":[460],"propos\u00e9e":[461],"Philippe":[463],"Biane,":[464],"utilisant":[466,633],"sommes":[468],"transpositions":[470],"l'alg\u00e8bre":[472],"groupe":[474,535,539],"sym\u00e9trique.":[475,551],"Avec":[476],"Florent":[477],"Benaych-Georges,":[478],"pu":[481],"g\u00e9n\u00e9raliser":[482],"r\u00e9sultats":[484,656],"P.":[486],"Biane":[487],"cycles":[490],"quelconques.":[491],"Notre":[492],"approche":[493,522],"combinatoire":[495],"d'aboutir":[501],"formules":[504],"explicites":[505],"pour":[506,593,639],"moments":[508],"cumulants":[511],"limite.":[517],"Gr\u00e2ce":[518],"m\u00eame":[521,605],"\u00e9labor\u00e9":[525],"analogue":[528],"classiques":[531],"rempla\u00e7ant":[533],"sym\u00e9trique":[536],"ab\u00e9lien":[540],"parties":[542],"d'un":[543],"ensemble":[544],"fini,":[545],"muni":[546],"l'op\u00e9ration":[548],"diff\u00e9rence":[550],"St\u00e9phane":[555],"Attal,":[556],"construit":[559],"approximation":[561,611],"Fock":[565,596,664],"libre":[566,580,589,647],"(qui":[567],"joue":[568],"r\u00f4le":[570],"central":[571],"non-commutatives)":[576],"produit":[579],"d\u00e9nombrable":[581],"d'espaces":[582],"discrets.":[583],"id\u00e9e":[585],"g\u00e9n\u00e9ralise":[586],"cas":[588,660],"similaire":[592],"sym\u00e9trique,":[597],"introduite":[598],"\u00e9tudi\u00e9":[600],"S.":[602],"Attal.":[603],"temps":[606],"obtenu":[609],"op\u00e9rateurs":[613,623],"fondamentaux":[614],"cr\u00e9ation,":[616],"d'annihilation":[617],"jauge":[620],"construits":[624],"partir":[626],"2.":[631],"constructions":[635],"ensuite":[637],"utilis\u00e9es":[638],"retrouver":[640],"quelques":[641],"approximations":[642],"connues":[643],"mouvement":[645],"brownien":[646],"processus":[650,672],"Poisson":[652],"libre.":[653],"Tous":[654],"g\u00e9n\u00e9ralisent":[658],"espaces":[662],"multiplicit\u00e9":[666],"sup\u00e9rieure,":[667],"permettent":[669],"d'approcher":[670],"multidimensionnels.":[673],"conclusion,":[675],"scientifiques":[679],"situe":[685],"trois":[689],"directions:":[691],"l'accent":[704],"\u00e9tant":[705],"mis":[706],"domaines.":[716]},"counts_by_year":[],"updated_date":"2026-11-01T11:40:01.658920","created_date":"2016-06-24T00:00:00"}