4
votes
1answer
112 views

Connection between degree of growth and return probabilities of random walks on Lie groups

Let $G$ be a finitely generated group of polynomial growth, let $\mu$ be a non-degenerate symmetric probability measure with finite support on $G$, and let $d$ be the degree of growth of $G$. ...
7
votes
2answers
603 views

Is there an algebraically normal function from $\mathbb{Z}^{n}$ to $\{ 0 , 1\}$?

Definition: Let $h$ be a polynomial in $n$ variables, then : $\gamma(h,r,R):=\{ v \in \mathbb{Z}^{n} : \vert h(v) \vert \leq r, \Vert v \Vert < R \}$ Let $\omega : \mathbb{Z}^{n} \to \{ 0 , ...
5
votes
1answer
453 views

Percolation in Cayley graphs of semigroups.

Percolation in Cayley graphs of groups are studied by many researchers. There are also the concept Cayley graphs for semigroups. Are there any research about percolation in Cayley graphs for ...