Related papers: Approximation of the effective conductivity of erg…

In this note we comment on the homogenization of a random elliptic operator in divergence form $-\nabla \cdot a\nabla$, where the coefficient field $a$ is distributed according to a stationary, but not necessarily ergodic, probability…

Let $\Omega$ be a Lipschitz domain in $\mathbb R^d$, and let $\mathcal A^\varepsilon=-\operatorname{div}A(x,x/\varepsilon)\nabla$ be a strongly elliptic operator on $\Omega$. We suppose that $\varepsilon$ is small and the function $A$ is…

Using tools from the theory of optimal transport, we establish several results concerning isometric actions of amenable topological groups with potentially unbounded orbits. Specifically, suppose $d$ is a compatible left-invariant metric on…

The purpose of this paper is to establish the almost sure weak ergodic convergence of a sequence of iterates $(x_n)$ given by $x_{n+1} = (I+\lambda_n A(\xi_{n+1},\,.\,))^{-1}(x_n)$ where $(A(s,\,.\,):s\in E)$ is a collection of maximal…

We study the homogenization problem for matrix strongly elliptic operators on $L_2(\mathbb R^d)^n$ of the form $\mathcal A^\varepsilon=-\operatorname{div}A(x,x/\varepsilon)\nabla$. The function $A$ is Lipschitz in the first variable and…

Let $(X, \mathcal{A},\mu)$ be a probability space and let $T$ be a contraction on $L^2(\mu)$. We provide suitable conditions over sequences $(w_k)$, $(u_k)$ and $(A_k)$ in such a way that the weighted ergodic limit…

For a continuous semicascade on a metrizable compact set $\Omega $, we consider the weak$^{*}$ convergence of generalized operator ergodic means in ${\rm End}\, \, C^{*} (\Omega)$. We discuss conditions on the dynamical system under which…

We report electrical conductivity $\sigma$ measurements on a range of two-dimensional electron gases (2DEGs) of varying linear extent. Intriguingly, at low temperatures ($T$) and low carrier density ($n_{\mathrm{s}}$) we find the behavior…

We define a random walk adic transformation associated to an aperiodic random walk on $G=\mathbb{Z}^{k}\times\mathbb{R}^{D-k}$ driven by a $\beta$-transformation and study its ergodic properties. In particular, this transformation is…

This paper is devoted to the quantitative homogenization of multiscale elliptic operator $-\nabla\cdot A_\varepsilon \nabla$, where $A_\varepsilon(x) = A(x/\varepsilon_1, x/\varepsilon_2,\cdots, x/\varepsilon_n)$, $\varepsilon =…

The present paper is a follow up of another one by A. O. Lopes, E. Oliveira and P. Thieullen which analyze ergodic transport problems. Our main focus will a more precise analysis of case where the maximizing probability is unique and is…

This paper studies numerical methods for the approximation of elliptic PDEs with lognormal coefficients of the form $-{\rm div}(a\nabla u)=f$ where $a=\exp(b)$ and $b$ is a Gaussian random field. The approximant of the solution $u$ is an…

In this paper, we consider numerical approximation to periodic measure of a time periodic stochastic differential equations (SDEs) under weakly dissipative condition. For this we first study the existence of the periodic measure $\rho_t$…

We investigate (uniform) mean ergodicity of weighted composition operators on the space of smooth functions and the space of distributions, both over an open subset of the real line. Among other things, we prove that a composition operator…

This paper deals with some self-interacting diffusions $(X_t,t\geq 0)$ living on $\mathbb{R}^d$. These diffusions are solutions to stochastic differential equations: \[\mathrm{d}X_t=\mathrm{d}B_t-g(t)\nabla…

We explain and restate the results from our recent paper arXiv:1503.08000.v3 in standard language for substitutions and $S$-adic systems in symbolic dynamics. We then produce as rather direct application an $S$-adic system (with finite set…

We approximate any portion of any orbit of the full diagonal group $A$ in the space of unimodular lattices in $\RR^n$ using a fixed proportion of a compact $A$-orbit. Using those approximations for the appropriate sequence of orbits, we…

Let $U$ be a unitary operator acting on the Hilbert space $\ch$, and $\a:\{1,..., 2k\}\mapsto\{1,..., k\}$ a pair partition. Then the ergodic average $$ \frac{1}{N^{k}}\sum_{n_{1},...,n_{k}=0}^{N-1} U^{n_{\a(1)}}A_{1}U^{n_{\a(2)}}...…

In the study of the observability of the wave equation (here on $(0,T)\times \mathbb{T}^d$, where $\mathbb{T}^d$ is the d-dimensional torus), a condition naturally emerges as a sufficient observability condition. This condition, which…

In this article, we consider the weighted ergodic optimization problem Axiom A attractors of a $C^2$ flow on a compact smooth manifold. The main result obtained in this paper is that for a generic observable from function space $\mc…