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关于随机矩阵的学术报告
发布时间: 2015-11-06     10:07   【返回上一页】 发布人:$curArticle.author


 1. Title : Sum rules and large deviations

Speaker: Alain Rouault (Université de Versailles-Saint-Quentin, France)

Abstract: We prove a Large Deviation Principle for the random spectral measure associated to the pair (HN,e) where HN is sampled in the GUE(N)and e is a fixed unit vector(and more generally in the extension of this model).

2. Title : Conditional limit theorems for products of random matrices

Speaker: Ion Grama (Université de Bretagne-Sud, France )

Abstract: Consider the product Gn=gn...g1 of the random matrices g1,...,gn in GL(d,R) and the random process Gnv=gn...g1v in Rd starting at point v∈Rd?{0}. It is well known that under appropriate assumptions, the sequence (log∥Gnv∥)n≥1 behaves like a sum of i.i.d./ r.v.'s and satisfies standard classical properties such as the law of large numbers, law of iterated logarithm and the central limit theorem. Denote by B the closed unit ball in Rd and by Bc its complement. For any v∈Bc define the exit time of the random process Gnv from Bc by τv=min{n≥1:Gnv∈B}. We establish the asymptotic as n→∞ of the probability of the event {τv>n} and find the limit law for the quantity 1n√log∥Gnv∥ conditioned that τv>n.

 

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