Valleys and the maximum local time for random walk in random environment

Amir Dembo, Nina Gantert, Yuval Peres +1

Let $\xi (n,x)$ be the local time at $x$ for a recurrent one-dimensional random walk in random environment after $n$ steps, and consider the maximum ${\xi }^{\ast }(n)={\max }_x\xi (n,x)$. It is k…