Random walks on abelian groups

Random Walks on Finite Groups

Markov chains on finite sets are used in a great variety of situations to approximate, understand and sample from their limit distribution. A familiar example is provided by card shuffling methods. From this viewpoint, one is interested in the “mixing time” of the chain, that is, the time at which the chain gives a good approximation of the limit distribution. A remarkable phenomenon known as t...

Random walks on finite rank solvable groups

Abstract. We establish the lower bound p2t(e, e) exp(−t1/3), for the large times asymptotic behaviours of the probabilities p2t(e, e) of return to the origin at even times 2t, for random walks associated with finite symmetric generating sets of solvable groups of finite Prüfer rank. (A group has finite Prüfer rank if there is an integer r , such that any of its finitely generated subgroup admit...

An introduction to random walks on groups

Random Walks on Finite Quantum Groups

1 Markov chains and random walks in classical probability . . 3 2 Quantum Markov chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 Random walks on comodule algebras . . . . . . . . . . . . . . . . . . . . . . 7 4 Random walks on finite quantum groups . . . . . . . . . . . . . . . . . . 11 5 Spatial Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . ....

CLT for random walks of commuting endomorphisms on compact abelian groups

Let S be an abelian group of automorphisms of a probability space (X,A, μ) with a finite system of generators (A1, ..., Ad). Let A l denote A1 1 ...A ld d , for l = (l1, ..., ld). If (Zk) is a random walk on Z , one can study the asymptotic distribution of the sums ∑n−1 k=0 f ◦AZk(ω) and ∑ l∈Z P(Zn = l)A f , for a function f on X . In particular, given a random walk on commuting matrices in SL(...