We present an analytic technique for estimating the growth for groups of intermediate growth. We apply our technique to Grigorchuk groups, which are the only known examples of such groups. Ourâ€¦ (More)

A ribbon polyomino is a polyomino which has at most one square (i, j) in every diagonal i& j=c. A tetromino is a polyomino with four squares. Up to translations there are exactly 8 different ribbonâ€¦ (More)

Let pc(G) be the critical probability of the site percolation on the Cayley graph of groupG. In [2] of Benjamini and Schramm conjectured thatpc < 1, given the group is infinite and not a finiteâ€¦ (More)

In this paper we extend the construction of random walks with a prescribed Poisson boundary found in [CM04] to the case of measures in the class of a generalized Gibbs state. The price for droppingâ€¦ (More)

We consider the universal Grigorchuk 2-group, i.e., the group such that every Grigorchuk 2-group is a quotient. We show that this group has a nice universal representation in the group of allâ€¦ (More)