Large Deviations for a Random Walk in Random Environment
Large Deviations for a Random Walk in Random Environment
Let $\omega = (p_x)_{x\in\mathbb{Z}}$ be an i.i.d. collection of (0, 1)-valued random variables. Given $\omega$, let $(X_n)_{n \geq 0}$ be the Markov chain on $\mathbb{Z}$ defined by $X_0 = 0$ and $X_{n + 1} = X_n + 1(\operatorname{resp}. X_n - 1)$ with probability $p_{X_n}(\operatorname{resp}.1 - p_{X_n})$. It is shown that …