All Questions

Question in brief Let $a$ and $b$ be unit vectors in $\mathbb{R}^d$. Let $f$ be the $1-step$ transition function of a random walk on the $d$ dimensional unit sphere. I am interested in evaluating $\...

For every positive integer $n$, consider a regular hexagon $\mathrm{H}_n$ such that the distance of each vertex from the center is $\frac{1}{\sqrt{n}}$. That in turn induces a tiling of $\mathbb{R}^...

Imagine I have unbounded $d$-dimensional integer lattice where I take two vertices, $v_a$ and $v_b$, separated by a fixed Manhattan distance $L$, and I release a random walker at $v_a$ and allow for ...