Large deviation principle for some beta ensembles

Dinh, Tien-Cuong; Nguyên, Viêt-Anh

Type de document :

Article dans une revue scientifique: Article original

DOI :

10.1090/tran/7171

Titre :

Large deviation principle for some beta ensembles

Auteur(s) :

Dinh, Tien-Cuong [Auteur]
National University of Singapore [NUS]
Nguyên, Viêt-Anh [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Titre de la revue :

Transactions of the American Mathematical Society
LPP-MATH

Pagination :

6565-6584

Éditeur :

American Mathematical Society

Date de publication :

2018-02-26

ISSN :

0002-9947

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

Let L be a positive line bundle over a projective complex manifoldX, Lp its tensor power of order p, H 0 (X, Lp ) the space of holomorphic sectionsof Lp , and Np the complex dimension of H 0 (X, Lp ). The determinant of a ...
Lire la suite >Let L be a positive line bundle over a projective complex manifoldX, Lp its tensor power of order p, H 0 (X, Lp ) the space of holomorphic sectionsof Lp , and Np the complex dimension of H 0 (X, Lp ). The determinant of a basisof H 0 (X, Lp ), together with some given probability measure on a weightedcompact set in X, induces naturally a β-ensemble, i.e., a random Np -pointprocess on the compact set. Physically, depending on X and the value of β,this general setting corresponds to a gas of free or interacting fermions on Xand may admit an interpretation in terms of some random matrix models.The empirical measures, associated with such β-ensembles, converge almostsurely to an equilibrium measure when p goes to inﬁnity. We establish alarge deviation theorem (LDT) with an eﬀective speed of convergence for theseempirical measures. Our study covers a large class of β-ensembles on a compactsubset of the unit sphere Sn ⊂ Rn+1 or of the Euclidean space Rn .Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Projet ANR :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :