Tianyi Zheng

Random walks and isoperimetric profiles under moment conditions

Let

Speed of random walks, isoperimetry and compression of finitely generated groups

G

Isoperimetric profiles and random walks on some permutation wreath products

be a finitely generated group equipped with a finite symmetric generating set and the associated word length function

Random walks on free solvable groups

|\cdot |

Random walks on nilpotent groups driven by measures supported on powers of generators

. We study the behavior of the probability of return for random walks driven by symmetric measures

On some random walks driven by spread-out measures

\mu

Large deviations for stable like random walks on

that are such that

\mathbb Z^d

\sum \rho(|x|)\mu(x) 0

with applications to random walks on wreath products

. For this purpose we develop new relations between the isoperimetric profiles associated with different symmetric probability measures. These techniques allow us to obtain a sharp

Infinitely supported Liouville measures of Schreier graphs

L^2