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- SARA BROFFERIO
- 2005

We determine all positive harmonic functions for a large class of " semi-isotropic " random walks on the lamplighter group, i.e., the wreath product Z q ≀ Z, where q ≥ 2. This is possible via the geometric realization of a Cayley graph of that group as the Diestel-Leader graph DL(q, q). More generally, DL(q, r) (q, r ≥ 2) is the horocyclic product of two… (More)

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… (More)

The Lie group Sol(p, q) is the semidirect product induced by the action of R on R 2 which is given by (x, y) → (e pz x, e −qz y), z ∈ R. Viewing Sol(p, q) as a 3-dimensional manifold, it carries a natural Riemannian metric and Laplace-Beltrami operator. We add a linear drift term in the z-variable to the latter, and study the associated Brownian motion with… (More)

The Lie group Sol(p, q) is the semidirect product induced by the action of R on R 2 which is given by (x, y) → (e pz x, e −qz y), z ∈ R. Viewing Sol(p, q) as a 3-dimensional manifold, it carries a natural Riemannian metric and Laplace-Beltrami operator. We add a linear drift term in the z-variable to the latter, and study the associated Brownian motion with… (More)

- SARA BROFFERIO
- 2009

We construct the Poisson boundary for a random walk supported by the general linear group on the rational numbers as the product of flag man-ifolds over the p-adic fields. To this purpose, we prove a law of large numbers using the Oseledets' multiplicative ergodic theorem. The only assumption we need is some moment condition on the measure governing the… (More)

We present simple proofs of transience/recurrence for certain card shuffling models, that is, random walks on the infinite symmetric group. In this note, we consider several models of shuffling an infinite deck of cards. One of these models has been considered previously by Lawler [La]; our methods (using flows, shorting and comparison of Dirichlet forms)… (More)

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