All Questions

Let $G$ be a finitely generated group and let $\mu$ be a finite measure on $G$. Define the Green function as $$G(\mu)=\sum_{n\geq 0}\mu^{*n}(e),$$ where $\mu^{*n}$ is the $n$th convolution power of $\...

Given a graph $G$ and a function $f:G\to\mathbb R$, we say that $f$ is harmonic if $$f(x)=\frac{1}{|N(x)|}\sum_{y\in N(x)}f(y)$$ for every $x\in G$, where $N(x)$ denotes the set of neighbors of $G$. ...

I am having difficulty in proving the lower bound of the discrete Poisson kernel of a square denoted as $H$ described below. It is stated in Gregory F. Lawler's Randomm Walk and the Heat Equation as ...