Random walks on groups and random transformations

This survey consists of three sections. The first one is about products of i.i.d. matrices: it discusses Lyapunov exponents, questions of positivity of the top Lyapunov exponent, siplicity of the spectrum, regularity and Central Limit theorems. In the second section we discuss random walks on general groups: questions of recurrence, harmonic functions, Poisson boundary and notions of entropy associated with random walks. The third section is concerned with compositions of random transformations of a space. The survey contains proofs or sketches of proofs for most of the results.

Authors: A. Furman,Bibliographical: Handbook of dynamical systems, Vol. 1A, 931--1014, North-Holland, Amsterdam, 2002.

Download: pdf

[Papers] [Alex Furman]