### Speaker

Dr
Hoang Chuong LAM
(Can Tho University)

### Description

We prove the quenched central limit theorem and the law of large numbers for reversible random walks in a stationary random environment on $Z$. In this model, the conductivity of the edge between $[k; k+1]$ is equal to $\alpha_{k} c(T^{k}\omega)$, where $\alpha_{k}$ be a positive number and $c$ be a positive measurable function on $\Omega.$
Fix $\omega \in \Omega,$ we consider the Poisson equation $(P_{\omega}-I)f=\psi$, and then use the pointwise ergodic theorem to treat the limit of solutions and then the limit theorems will be established by the convergence of moments.
Depauw, J and Derrien, J.-M. (2009). Variance limite d'une marche aléatoire réversible en milieu aléatoire sur ${Z}$. C. R. Acad. Sci. Paris, Ser. I. 347 p.401-406.
Lam, H.-C. (2014). Quenched central limit theorem for reversible random waks in random environment on
${Z}$. Journal of Applied Probability. 51 1-14.

### Primary author

Dr
Hoang Chuong LAM
(Can Tho University)