2 problems

Let $D\subset\mathbb{R}^2$ be a convex domain symmetric with respect to both coordinate axes. Let $\lambda_n$ and $\varphi_n$ be the eigenvalues and eigenfunctions of the Cauchy pr…

Let $(X_i)$ be a sequence of independent identically distributed integer-valued random variables with … where $C$ is a normalizing constant. Define the random walk…