We study in this paper some combinatorial invariants associated with ergodic actions of infinite, countable (discrete) groups. Let (X,μ) be a standard probability space and Γ an infinite, countable group with a set of generators 1 / ∈ S ⊆ Γ. Given a free, measure-preserving action a of Γ on (X,μ), we consider the graph G(S, a) = (X,E(S, a)), whose vertices are the points in X and where x 6= y ∈...

We investigate the ergodic capacity of amplify-andforward (AF) dual-hop relaying systems in composite Nakagamim/Inverse-Gaussian fading channels. This type of fading, which is known in the literature as G fading, has recently attracted increasing research interest thanks to its ability to better approximate the Nakagami-m/lognormal model compared to the Nakagami-m/gamma model. We study both fix...

We study the homogenization of a G-equation which is advected by a divergence free stationary vector field in a general ergodic random environment. We prove that the averaged equation is an anisotropic deterministic G-equation and we give necessary and sufficient conditions in order to have enhancement. Since the problem is not assumed to be coercive it is not possible to have uniform bounds fo...

We determine the limit distribution (as λ → ∞) of complex zeros for holomorphic continuations φCλ to Grauert tubes of real eigenfunctions of the Laplacian on a real analytic compact Riemannian manifold (M, g) with ergodic geodesic flow. If {φjk} is an ergodic sequence of eigenfunctions, we prove the weak limit formula 1 λj φjk ] → i π∂∂|ξ|g, where φjk ] is the current of integration over the co...

Introduction. An interesting but apparently neglected generalization due to Doob [l], of the ergodic theorem, is the generalization to transformations which are not necessarily one-to-one. In his paper [l], Doob showed that the transformation of the interval [0, l] into itself given by/(x) =nx (modulo 1), where n — 1 is a positive integer, is ergodic under Lebesgue measure and that the law of l...

Let μ be a probability measure on a locally compact group G, and suppose G acts measurably on a probability measure space (X,m), preserving the measure m. We study ergodic theoretic properties of the action along μ-i.i.d. random walks on G. It is shown that under a (necessary) spectral assumption on the μ-averaging operator on L2(X,m), almost surely the mean and the pointwise (Kakutani’s) rando...

By making fundamental use of the Farey shift map and employing infinite (but σ-finite) measures together with the Chacon-Ornstein ergodic theorem it is possible to find new metrical results for continued fractions. Moreover this offers a unified approach to several existing theorems. The application of ergodic theory to the study of continued fractions began with the Gauss transformation, G: [0...

We prove that an arbitrary (not necessarily countably generated) Hilbert G −A module on a G − C∗ algebra A admits an equivariant embedding into a trivial G−A module, provided G is a compact Lie group and its action on A is ergodic.

Modeling the traffic flow at signalized intersections has been discussed in many works [1][2][3][4]. Though streets and intersections and designed to be Ergodic, the traffic flow during busy hours is not necessarily Ergodic. In this paper, we modeled the traffic at intersection during busy hours by using M/G/1 model. And based on the collected data, we modeled a special service distribution pat...

Given an approach region Γ ∈ Z+ and a pair U , V of commuting nonperiodic measure preserving transformations on a probability space (Ω,Σ, μ), it is shown that either the associated multiparameter ergodic averages of any function in L(Ω) converge a.e. or that, given a positive increasing function φ on [0,∞) that is o(log x) as x → ∞, there exists a function g ∈ Lφ(L) (Ω) whose associated multipa...