3 problems

Let $\mathbf{e}_1,\mathbf{e}_2$ be the usual basis of $\mathbb{Z}^2$. Let $\mathbf{Y}=(\{\pm\mathbf{e}_1,\pm\mathbf{e}_2\}^{\mathbb{Z}},\nu,S)$ be the Bernoulli shift with…

Let $(\mathbf{Y},\sigma)$ be the system and cocycle corresponding to a $p$-stable random walk on $\mathbb{Z}$ for some $p\in(1,2)$, let $\mathbf{X}$ be a Bernoulli flow, and let…

Let $c$ be a scenery and let $(y_0,y_1,\ldots)$ be a random-walk trajectory. Suppose that the scenery patch $c|_{[-m;m]}$ is to be reconstructed from the observed output string…