EuDML | Browse

We show that the only random orderings of finite graphs that are invariant under isomorphism and induced subgraph are the uniform random orderings. We show how this implies the unique ergodicity of the automorphism group of the random graph. We give similar theorems for other structures, including, for example, metric spaces. These give the first examples of uniquely ergodic groups, other than compact groups and extremely amenable groups, after Glasner andWeiss’s example of the group of all permutations...

Random walks on the affine group of local fields and of homogeneous trees

Donald I. Cartwright, Vadim A. Kaimanovich, Wolfgang Woess (1994)

Annales de l'institut Fourier

The affine group of a local field acts on the tree $𝕋 (𝔉)$ (the Bruhat-Tits building of $GL (2, 𝔉)$ ) with a fixed point in the space of ends $\partial 𝕋 (F)$ . More generally, we define the affine group $Aff (𝔉)$ of any homogeneous tree $𝕋$ as the group of all automorphisms of $𝕋$ with a common fixed point in $\partial 𝕋$ , and establish main asymptotic properties of random products in $Aff (𝔉)$ : (1) law of large numbers and central limit theorem; (2) convergence to $\partial 𝕋$ and solvability of the Dirichlet problem at infinity; (3) identification of the Poisson boundary...

Rankin triple L functions

I. Piatetski-Shapiro, Stephen Rallis (1987)

Compositio Mathematica

Rankin–Cohen brackets and representations of conformal Lie groups

Michael Pevzner (2012)

Annales mathématiques Blaise Pascal

This is an extended version of a lecture given by the author at the summer school “Quasimodular forms and applications” held in Besse in June 2010.The main purpose of this work is to present Rankin-Cohen brackets through the theory of unitary representations of conformal Lie groups and explain recent results on their analogues for Lie groups of higher rank. Various identities verified by such covariant bi-differential operators will be explained by the associativity of a non-commutative product...