Sara Brofferio

Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel-Leader graphs ✩

Abstract We determine the precise asymptotic behaviour (in space) of the Green kernel of simple random walk with drift on the Diestel–Leader graph DL ( q , r ) , where q , r ⩾ 2 . The latter is the horocyclic product of two homogeneous trees with respective degrees q + 1 and r + 1 . When q = r , it is the Cayley graph of the wreath product (lamplighter group) Z q ≀ Z with respect to a natural set of generators. We describe the full Martin compactification of these random walks on DL -graphs and, in particular, lamplighter groups. This completes previous results of Woess, who has determined all minimal positive harmonic functions.

On unbounded invariant measures of stochastic dynamical systems

We consider stochastic dynamical systems on

Brownian Motion and Harmonic Functions on Sol(p,q)

{\mathbb{R}}

On the invariant measure of the random difference equation Xn = AnXn−1 + Bn in the critical case

, that is, random processes defined by

On transience of card shuffling

X_n^x=\Psi_n(X_{n-1}^x)

On Solutions of the Affine Recursion and the Smoothing Transform in the Critical Case

,

How a centred random walk on the affine group goes to infinity

X_0^x=x

Internal Diffusion Limited Aggregation on Discrete Groups Having Exponential Growth

, where

Positive Harmonic Functions for Semi-Isotropic Random Walks on Trees, Lamplighter Groups, and DL-Graphs

\Psi _n

Poisson boundary of GLd(ℚ)

are i.i.d. random continuous transformations of some unbounded closed subset of