Large deviation principle for some beta ensembles

Dinh, Tien-Cuong; Nguyên, Viêt-Anh

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1090/tran/7171

Title :

Large deviation principle for some beta ensembles

Author(s) :

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

Journal title :

Transactions of the American Mathematical Society
LPP-MATH

Pages :

6565-6584

Publisher :

American Mathematical Society

Publication date :

2018-02-26

ISSN :

0002-9947

HAL domain(s) :

Mathématiques [math]

English abstract : [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 ...
Show more >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 .Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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