Nathanaël Enriquez

Edge oriented reinforced random walks and RWRE

Abstract The aim of this text is to present, in a general framework, a precise and explicit correspondance between a class of edge oriented reinforced random walks and random walks in random environment. To cite this article: N. Enriquez, C. Sabot, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 941–946.

Markov Chains on Graphs and Brownian Motion

AbstractWe consider random walks with small fixed steps inside of edges of a graph

Statistic of the winding of geodesics on a Riemann surface with finite area and constant negative curvature

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Quenched limits for the fluctuations of transient random walks in random environment on Z

, prescribing a natural rule of probabilities of jumps over a vertex. We show that after an appropriate rescaling such random walks weakly converge to the natural Brownian motion on

Asymptotic expansion of the expected spectral measure of Wigner matrices

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Canonical Lift and Exit Law of the Fundamental Diffusion Associated with a Kleinian Group

constructed in Ref. 1.