Products of unimodular independent random matrices

Abstract

Contents Introduction 1. Formulation of the problem 2. Survey of results 3. Basic results 4. Contents of the article §1. The phase space of a Markov chain 1. The space Y 2. Metric on Y 3. Group action of G on Y 4. Characteristic measures on Y §2. Strong law of large numbers 1. μ-random walk on Y 2. Ergodicity of the μ-random walk 3. Non-equality of Lyapunov exponents 4. Estimates of z(yg(n)) 5. Proof of Theorem 0.1 6. Rate of contraction to a point §3. Limit theorems for Markov chains 1. The Ionescu-Tulcea and Marinescu theorem 2. Perturbed Markov operators 3. Decomposition of Pη(τ) for small τ 4. Central limit theorem 5. Local limit theorem §4. Proof of the central and local limit theorems §5. Proof of the conditional limit theorem 1. Properties of the operator Kβ 2. Properties of the operator Pβ(τ) 3. Critical case 4. Proof of the conditional limit theorem Bibliography