Random walks on the discrete affine group

Isotropic Random Walks on Affine Buildings

Recently, Cartwright and Woess [5] provided a detailed analysis of isotropic random walks on the vertices of thick affine buildings of type Ãn. Their results generalise results of Sawyer [18] where homogeneous trees are studied (these are Ã1 buildings), and Lindlbauer and Voit [9], where Ã2 buildings are studied. In this paper we apply techniques of spherical harmonic analysis to prove a local ...

Random Walks on Dicyclic Group

In this paper I work out the rate of convergence of a non-symmetric random walk on the dicyclic group (Dicn) and that of its symmetric analogue on the same group. The analysis is via group representation techniques from Diaconis (1988) and closely follows the analysis of random walk on cyclic group in Chapter 3C of Diaconis. I find that while the mixing times (the time for the random walk to ge...

Random walks on the mapping class group

We show that a random walk on the mapping class group of an orientable surface gives rise to a pseudo-Anosov element with asymptotic probability one. Our methods apply to many subgroups of the mapping class group, including the Torelli group.

Random Walks on the Affine Group of Local Fields and of Homogeneous Trees

Random Walks on Discrete and Continuous Circles

We consider a large class of random walks on the discrete circle Z/(n), defined in terms of a piecewise Lipschitz function, and motivated by the “generation gap” process of Diaconis. For such walks, we show that the time until convergence to stationarity is bounded independently of n. Our techniques involve Fourier analysis and a comparison of the random walks on Z/(n) with a random walk on the...