Vietnamese - French conference in applied mathematics

Limit theorems for random walks in random environment

9 juil. 2018, 15:45

30m

Ho Chi Minh City University of Science

Orateur

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 $\mathrm{\Omega }.$ Fix $\omega \in \mathrm{\Omega },$ 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.