A QUENCHED CENTRAL LIMIT THEOREM FOR REVERSIBLE RANDOM WALKS IN A RANDOM ENVIRONMENT ON Z

作者：Hoang Chuong Lam^*

来源：Journal of Applied Probability, 2014, 51(4): 1051-1064.

DOI：10.1017/s0021900200011979

• Quenched central limit theorem
• reversible random walk in random environment

The main aim of this paper is to prove the quenched central limit theorem for reversible random walks in a stationary random environment on Z without having the integrability condition on the conductance and without using any martingale. The method shown here is particularly simple and was introduced by Depauw and Derrien [3]. More precisely, for a given realization omega of the environment, we consider the Poisson equation (P-omega-I)g = f, and then use the pointwise ergodic theorem in [8] to treat the limit of solutions and then the central limit theorem will be established by the convergence of moments. In particular, there is an analogue to a Markov process with discrete space and the diffusion in a stationary random environment.

• 出版日期2014-12