3 problems

Let $G$ be an abelian group, let $V\subseteq G$ be a symmetric set of generators, and let $\Delta$ be the corresponding symmetric-walk Laplacian. Let $\mathcal{L}$ be the generator…

Let $G$ be an abelian group and let a lifted random walk on $G$ be obtained by augmenting the position with a direction variable, producing a second-order Markov chain. Write…

Consider the lifted random walk on the discrete torus $\mathbb{Z}_n^d$ with fixed dimension $d$ and direction-change probability $p\in(0,1)$. Its relaxation time is denoted by…