9-11 July 2018
Ho Chi Minh City University of Science
Asia/Ho_Chi_Minh timezone

Limit theorems for random walks in random environment

9 Jul 2018, 15:45
30m
Ho Chi Minh City University of Science

Ho Chi Minh City University of Science

227 Nguyễn Văn Cừ, Phường 4, T.P. Hồ Chí Minh

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)

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