Large deviations for the largest eigenvalue of an Hermitian Brownian motion

Catherine Donati-Martin (1) , Mylène Maïda (2)

1 LMV - Laboratoire de Mathématiques de Versailles
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We establish a large deviation principle for the process of the largest eigenvalue of an Hermitian Brownian motion. By a contraction principle, we recover the LDP for the largest eigenvalue of a rank one deformation of the GUE.

Mots clés: stochastic calculus; Large deviations; Dyson Brownian motion; random matrices; stochastic calculus.

Domaines: Probabilités [math.PR]

Catherine Donati-Martin, Mylène Maïda. Large deviations for the largest eigenvalue of an Hermitian Brownian motion. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2012, 9 (2), pp.501-530. ⟨hal-00565889v2⟩