4 problems

Let $d=2$, let $X_n$ be a random walk in an i.i.d. uniformly elliptic random environment, and let $I_q:\mathbb R^2\to[0,\infty]$ be its quenched large deviation rate function. Writ…

Let $X_n$ be a random walk in an i.i.d. uniformly elliptic random environment on $\mathbb Z^2$, and let $P_{0,\omega}$ denote its quenched law. Under the specific scaling appropria…

Fix $t\in\mathbb Z$. In the half-space Beta random walk in random environment, define … for $x\in\mathbb Z_{\geqslant 0}$. Half-space Gamma-distribution conjecture. The limit exist…

Let $t\in\mathbb Z$ and consider the full-space Beta random walk in random environment. For each $x\in\mathbb Z$, let $\mathsf Z_t^{\mathbb Z}(x)$ denote the full-space point-to-li…