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Physique statistique des systèmes désordonnées en basses dimensions

Author: Xiangyu CaoAlberto RossoRaoul SantachiaraBertrand GeorgeotJonathan P KeatingAll authors
Publisher: 2017.
Dissertation: Thèse de doctorat : Physique : Université Paris-Saclay (ComUE) : 2017.
Edition/Format:   Computer file : Document : Thesis/dissertation : French
Summary:
Cette thèse présente des résultats nouveaux dans deux sujets de la physique statistique du désordre: les modèles aux energies aléatoires logarithmiquement corrélées (logREMs), et la transition de localisation dans les matrices aléatoires à longues portées.Dans la première partie consacrée aux logREMs, nous montrons comment décrire leurs points communs et les données spécifiques aux modèles
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Details

Genre/Form: Thèses et écrits académiques
Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Xiangyu Cao; Alberto Rosso; Raoul Santachiara; Bertrand Georgeot; Jonathan P Keating; Christopher Mudry; Didina Serban; Université Paris-Saclay (2015-2019).; École doctorale Physique en Île-de-France (Paris / 2014-....).; Université Paris-Sud (1970-2019).; Laboratoire de physique théorique et modèles statistiques (Orsay, Essonne / 1998-....).
OCLC Number: 990802154
Notes: Titre provenant de l'écran-titre.
Description: 1 online resource
Responsibility: Xiangyu Cao ; sous la direction de Alberto Rosso et de Raoul Santachiara.

Abstract:

Cette thèse présente des résultats nouveaux dans deux sujets de la physique statistique du désordre: les modèles aux energies aléatoires logarithmiquement corrélées (logREMs), et la transition de localisation dans les matrices aléatoires à longues portées.Dans la première partie consacrée aux logREMs, nous montrons comment décrire leurs points communs et les données spécifiques aux modèles particuliers. Ensuite nous appliquons la méthode de la brisure de symétrie des répliques pour les étudier en general, et en déduirons la transition vitreuse et le processus des minima, en termes de processus de Poisson décorés. Nous présentons également une série d'application des polynômes de Jack à la prédiction exactes des observables dans le modèle circulaire et ses variants. Finalement, nous décrivons les progrès récents sur la connexion exacte entre les logREMs et la théorie conforme de Liouville.La seconde partie a pour but d'introduire une nouvelle classe de matrices aléatoires à bandes, dite la classe des distributions larges; elle ressemble essentiellement aux matrices creuses. Nous étudions d'abord un modèle particulier de la classe, les matrices aléatoires Bêta, qui sont inspirées par une correspondence exacte à un modèle statistique récemment étudié, celui de la dynamique épidémique. A l'aide des arguments analytiques appuyés sur la correspondence et des simulations numériques, nous montrons l'existence des transitions de localisation avec des valeurs propres critiques dans le régime des paramètres dit d'exponentielle étirée. Ensuite, en utilisant une approche de renormalisation et de diagonalisation par blocs, nous soutenons que les transitions de localisation sont en général présentes dans la class des distributions larges.

This thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transition in long-range random matrices.In the first part devoted to logREMs, we show how to characterise their common properties and model--specific data. Then we develop their replica symmetry breaking treatment, which leads to the freezing scenario of their free energy distribution and the general description of their minima process, in terms of decorated Poisson point process. We also report a series of new applications of the Jack polynomials in the exact predictions of some observables in the circular model and its variants. Finally, we present the recent progress on the exact connection between logREMs and the Liouville conformal field theory.The goal of the second part is to introduce and study a new class of banded random matrices, the broadly distributed class, which is characterid an effective sparseness. We will first study a specific model of the class, the Beta Banded random matrices, inspired by an exact mapping to a recently studied statistical model of long--range first--passage percolation/epidemics dynamics. Using analytical arguments based on the mapping and numerics, we show the existence of localisation transitions with mobility edges in the ``stretch--exponential'' parameter--regime of the statistical models. Then, using a block--diagonalization renormalization approach, we argue that such localization transitions occur generically in the broadly distributed class.

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Primary Entity<\/h3>\n
<http:\/\/www.worldcat.org\/oclc\/990802154<\/a>> # Physique statistique des syst\u00E8mes d\u00E9sordonn\u00E9es en basses dimensions<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:MediaObject<\/a>, bgn:ComputerFile<\/a>, schema:CreativeWork<\/a>, bgn:Thesis<\/a> ;\u00A0\u00A0\u00A0\nbgn:inSupportOf<\/a> \"Th\u00E8se de doctorat : Physique : Universit\u00E9 Paris-Saclay (ComUE) : 2017.<\/span>\" ;\u00A0\u00A0\u00A0\nlibrary:oclcnum<\/a> \"990802154<\/span>\" ;\u00A0\u00A0\u00A0\nlibrary:placeOfPublication<\/a> <http:\/\/id.loc.gov\/vocabulary\/countries\/fr<\/a>> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Topic\/ordre_et_desordre_physique<\/a>> ; # Ordre et d\u00E9sordre (physique)<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Thing\/desordre<\/a>> ; # D\u00E9sordre<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Topic\/transition_vitreuse<\/a>> ; # Transition vitreuse<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Thing\/statistique_d_extremes<\/a>> ; # Statistique d\'extr\u00EAmes<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Topic\/valeurs_extremes_theorie_des<\/a>> ; # Valeurs extr\u00EAmes, Th\u00E9orie des<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Topic\/anderson_modele_d<\/a>> ; # Anderson, Mod\u00E8le d\'<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Thing\/invariance_conforme<\/a>> ; # Invariance conforme<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Thing\/matrices_aleatoires_a_bandes<\/a>> ; # Matrices al\u00E9atoires \u00E0 bandes<\/span>\n\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Thing\/transition_de_localisation<\/a>> ; # Transition de localisation<\/span>\n\u00A0\u00A0\u00A0\nschema:author<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Person\/cao_xiangyu_1989<\/a>> ; # Xiangyu Cao<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Organization\/ecole_doctorale_physique_en_ile_de_france_paris_2014<\/a>> ; # \u00C9cole doctorale Physique en \u00CEle-de-France (Paris \/ 2014-....).<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Organization\/universite_paris_sud_1970_2019<\/a>> ; # Universit\u00E9 Paris-Sud (1970-2019).<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Person\/keating_jonathan_p<\/a>> ; # Jonathan P Keating<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Organization\/laboratoire_de_physique_theorique_et_modeles_statistiques_orsay_essonne_1998<\/a>> ; # Laboratoire de physique th\u00E9orique et mod\u00E8les statistiques (Orsay, Essonne \/ 1998-....).<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Person\/santachiara_raoul_1975<\/a>> ; # Raoul Santachiara<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Organization\/universite_paris_saclay_2015_2019<\/a>> ; # Universit\u00E9 Paris-Saclay (2015-2019).<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Person\/georgeot_bertrand_19<\/a>> ; # Bertrand Georgeot<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Person\/mudry_christopher_1962<\/a>> ; # Christopher Mudry<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Person\/rosso_alberto_1974<\/a>> ; # Alberto Rosso<\/span>\n\u00A0\u00A0\u00A0\nschema:contributor<\/a> <http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Person\/serban_didina_19<\/a>> ; # Didina Serban<\/span>\n\u00A0\u00A0\u00A0\nschema:datePublished<\/a> \"2017<\/span>\" ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"This thesis presents original results in two domains of disordered statistical physics: logarithmic correlated Random Energy Models (logREMs), and localization transition in long-range random matrices.In the first part devoted to logREMs, we show how to characterise their common properties and model--specific data. Then we develop their replica symmetry breaking treatment, which leads to the freezing scenario of their free energy distribution and the general description of their minima process, in terms of decorated Poisson point process. We also report a series of new applications of the Jack polynomials in the exact predictions of some observables in the circular model and its variants. Finally, we present the recent progress on the exact connection between logREMs and the Liouville conformal field theory.The goal of the second part is to introduce and study a new class of banded random matrices, the broadly distributed class, which is characterid an effective sparseness. We will first study a specific model of the class, the Beta Banded random matrices, inspired by an exact mapping to a recently studied statistical model of long--range first--passage percolation\/epidemics dynamics. Using analytical arguments based on the mapping and numerics, we show the existence of localisation transitions with mobility edges in the ``stretch--exponential\'\' parameter--regime of the statistical models. Then, using a block--diagonalization renormalization approach, we argue that such localization transitions occur generically in the broadly distributed class.<\/span>\"@fr<\/a> ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"Cette th\u00E8se pr\u00E9sente des r\u00E9sultats nouveaux dans deux sujets de la physique statistique du d\u00E9sordre: les mod\u00E8les aux energies al\u00E9atoires logarithmiquement corr\u00E9l\u00E9es (logREMs), et la transition de localisation dans les matrices al\u00E9atoires \u00E0 longues port\u00E9es.Dans la premi\u00E8re partie consacr\u00E9e aux logREMs, nous montrons comment d\u00E9crire leurs points communs et les donn\u00E9es sp\u00E9cifiques aux mod\u00E8les particuliers. Ensuite nous appliquons la m\u00E9thode de la brisure de sym\u00E9trie des r\u00E9pliques pour les \u00E9tudier en general, et en d\u00E9duirons la transition vitreuse et le processus des minima, en termes de processus de Poisson d\u00E9cor\u00E9s. Nous pr\u00E9sentons \u00E9galement une s\u00E9rie d\'application des polyn\u00F4mes de Jack \u00E0 la pr\u00E9diction exactes des observables dans le mod\u00E8le circulaire et ses variants. Finalement, nous d\u00E9crivons les progr\u00E8s r\u00E9cents sur la connexion exacte entre les logREMs et la th\u00E9orie conforme de Liouville.La seconde partie a pour but d\'introduire une nouvelle classe de matrices al\u00E9atoires \u00E0 bandes, dite la classe des distributions larges; elle ressemble essentiellement aux matrices creuses. Nous \u00E9tudions d\'abord un mod\u00E8le particulier de la classe, les matrices al\u00E9atoires B\u00EAta, qui sont inspir\u00E9es par une correspondence exacte \u00E0 un mod\u00E8le statistique r\u00E9cemment \u00E9tudi\u00E9, celui de la dynamique \u00E9pid\u00E9mique. A l\'aide des arguments analytiques appuy\u00E9s sur la correspondence et des simulations num\u00E9riques, nous montrons l\'existence des transitions de localisation avec des valeurs propres critiques dans le r\u00E9gime des param\u00E8tres dit d\'exponentielle \u00E9tir\u00E9e. Ensuite, en utilisant une approche de renormalisation et de diagonalisation par blocs, nous soutenons que les transitions de localisation sont en g\u00E9n\u00E9ral pr\u00E9sentes dans la class des distributions larges.<\/span>\"@fr<\/a> ;\u00A0\u00A0\u00A0\nschema:exampleOfWork<\/a> <http:\/\/worldcat.org\/entity\/work\/id\/4391467411<\/a>> ;\u00A0\u00A0\u00A0\nschema:genre<\/a> \"Th\u00E8ses et \u00E9crits acad\u00E9miques<\/span>\"@fr<\/a> ;\u00A0\u00A0\u00A0\nschema:inLanguage<\/a> \"fr<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Physique statistique des syst\u00E8mes d\u00E9sordonn\u00E9es en basses dimensions<\/span>\"@fr<\/a> ;\u00A0\u00A0\u00A0\nschema:productID<\/a> \"990802154<\/span>\" ;\u00A0\u00A0\u00A0\nschema:url<\/a> <https:\/\/tel.archives-ouvertes.fr\/tel-01545931<\/a>> ;\u00A0\u00A0\u00A0\nschema:url<\/a> <http:\/\/www.theses.fr\/2017SACLS067\/document<\/a>> ;\u00A0\u00A0\u00A0\nwdrs:describedby<\/a> <http:\/\/www.worldcat.org\/title\/-\/oclc\/990802154<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

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<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Organization\/laboratoire_de_physique_theorique_et_modeles_statistiques_orsay_essonne_1998<\/a>> # Laboratoire de physique th\u00E9orique et mod\u00E8les statistiques (Orsay, Essonne \/ 1998-....).<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Organization<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Laboratoire de physique th\u00E9orique et mod\u00E8les statistiques (Orsay, Essonne \/ 1998-....).<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
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<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Person\/keating_jonathan_p<\/a>> # Jonathan P Keating<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Keating<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Jonathan P.<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Jonathan P Keating<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Person\/mudry_christopher_1962<\/a>> # Christopher Mudry<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"1962<\/span>\" ;\u00A0\u00A0\u00A0\nschema:deathDate<\/a> \"\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Mudry<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Christopher<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Christopher Mudry<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Person\/rosso_alberto_1974<\/a>> # Alberto Rosso<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"1974<\/span>\" ;\u00A0\u00A0\u00A0\nschema:deathDate<\/a> \"\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Rosso<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Alberto<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Alberto Rosso<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
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<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Person\/serban_didina_19<\/a>> # Didina Serban<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Person<\/a> ;\u00A0\u00A0\u00A0\nschema:birthDate<\/a> \"19..<\/span>\" ;\u00A0\u00A0\u00A0\nschema:deathDate<\/a> \"\" ;\u00A0\u00A0\u00A0\nschema:familyName<\/a> \"Serban<\/span>\" ;\u00A0\u00A0\u00A0\nschema:givenName<\/a> \"Didina<\/span>\" ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Didina Serban<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Thing\/desordre<\/a>> # D\u00E9sordre<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"D\u00E9sordre<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Thing\/invariance_conforme<\/a>> # Invariance conforme<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Invariance conforme<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Thing\/matrices_aleatoires_a_bandes<\/a>> # Matrices al\u00E9atoires \u00E0 bandes<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Matrices al\u00E9atoires \u00E0 bandes<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Thing\/statistique_d_extremes<\/a>> # Statistique d\'extr\u00EAmes<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Statistique d\'extr\u00EAmes<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Thing\/transition_de_localisation<\/a>> # Transition de localisation<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Thing<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Transition de localisation<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Topic\/anderson_modele_d<\/a>> # Anderson, Mod\u00E8le d\'<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Anderson, Mod\u00E8le d\'<\/span>\"@fr<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Topic\/ordre_et_desordre_physique<\/a>> # Ordre et d\u00E9sordre (physique)<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Ordre et d\u00E9sordre (physique)<\/span>\"@fr<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Topic\/transition_vitreuse<\/a>> # Transition vitreuse<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Transition vitreuse<\/span>\"@fr<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/experiment.worldcat.org\/entity\/work\/data\/4391467411#Topic\/valeurs_extremes_theorie_des<\/a>> # Valeurs extr\u00EAmes, Th\u00E9orie des<\/span>\n\u00A0\u00A0\u00A0\u00A0a \nschema:Intangible<\/a> ;\u00A0\u00A0\u00A0\nschema:name<\/a> \"Valeurs extr\u00EAmes, Th\u00E9orie des<\/span>\"@fr<\/a> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/id.loc.gov\/vocabulary\/countries\/fr<\/a>>\u00A0\u00A0\u00A0\u00A0a \nschema:Place<\/a> ;\u00A0\u00A0\u00A0\ndcterms:identifier<\/a> \"fr<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.theses.fr\/2017SACLS067\/document<\/a>>\u00A0\u00A0\u00A0\nrdfs:comment<\/a> \"Acc\u00E8s au texte int\u00E9gral<\/span>\" ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n
<http:\/\/www.worldcat.org\/title\/-\/oclc\/990802154<\/a>>\u00A0\u00A0\u00A0\u00A0a \ngenont:InformationResource<\/a>, genont:ContentTypeGenericResource<\/a> ;\u00A0\u00A0\u00A0\nschema:about<\/a> <http:\/\/www.worldcat.org\/oclc\/990802154<\/a>> ; # Physique statistique des syst\u00E8mes d\u00E9sordonn\u00E9es en basses dimensions<\/span>\n\u00A0\u00A0\u00A0\nschema:dateModified<\/a> \"2020-05-24<\/span>\" ;\u00A0\u00A0\u00A0\nvoid:inDataset<\/a> <http:\/\/purl.oclc.org\/dataset\/WorldCat<\/a>> ;\u00A0\u00A0\u00A0\u00A0.\n\n\n<\/div>\n\n

Content-negotiable representations<\/p>\n