Related papers: Poisson-Orlicz norm and infinite Ergodic Theory

Let $k \ge 1$ be an integer and $f$ a holomorphic endomorphism of $\mathbb P^k (\mathbb C)$ of algebraic degree $d\geq 2$. We introduce a volume dimension for ergodic $f$-invariant probability measures with strictly positive Lyapunov…

We introduce an ergodic approach to the study of {\em joint normality} of representations of numbers. For example, we show that for any integer $b \geq 2$ almost every number $x \in [0,1)$ is jointly normal with respect to the $b$-expansion…

We extend a recent result of Tim Austin (see arXiv:0905.0515) to the L^1 setting, thus providing a general version of the Birkhoff ergodic theorem for functions taking values in nonpositively curved spaces. In this setting, the notion of a…

This paper aims to extend the concept of stochastic $\Sigma$-convergence to the framework of Orlicz-Sobolev spaces in order to deals with coupled stochastic and deterministic homogenization problems in this type of spaces. Thus, this…

We consider random fields indexed by finite subsets of an amenable discrete group, taking values in the Banach-space of bounded right-continuous functions. The field is assumed to be equivariant, local, coordinate-wise monotone, and almost…

We study stochastic Euler equations in both compressible and incompressible regimes, on the whole space and on the torus, driven by genuinely mixed multiplicative noise: continuous Stratonovich/It\^o components and a discontinuous Marcus…

For a noncommutative Orlicz space associated with a semifnite von Neumann algebra, a faithful normal semifnite trace and an Orlicz function satisfying $(\delta_2,\Delta_2)-$condition, an individual ergodic theorem is proved.

We establish a general theory of optimal strong error estimation for numerical approximations of a second-order parabolic stochastic partial differential equation with monotone drift driven by a multiplicative infinite-dimensional Wiener…

A new characterization of the exponential type Orlicz spaces generated by the functions $\exp(|x|^p)-1$ ($p\ge 1$) is given. We define norms for centered random variables belonging to these spaces. We show equivalence of these norms with…

We define a notion of logarithmic, Coulomb and Riesz interactions in any dimension for random systems of infinite charged point configurations with a uniform background of opposite sign. We connect this interaction energy with the…

In [17] the author and A. Vershik have shown that for $\be=\frac12(1+\sqrt5)$ and the alphabet $\{0,1\}$ the infinite Bernoulli convolution ($=$ the Erd\"os measure) has a property similar to the Lebesgue measure. Namely, it is…

The link between 3D spaces with (in general, non-constant) curvature and quantum deformations is presented. It is shown how the non-standard deformation of a sl(2) Poisson coalgebra generates a family of integrable Hamiltonians that…

We initiate the study of effective pointwise ergodic theorems in resource-bounded settings. Classically, the convergence of the ergodic averages for integrable functions can be arbitrarily slow. In contrast, we show that for a class of…

We study strictly ergodic Delone dynamical systems and prove an ergodic theorem for Banach space valued functions on the associated set of pattern classes. As an application, we prove existence of the integrated density of states in the…

Let $H$ be the space of all Hermitian matrices of infinite order and $U(\infty)$ be the inductive limit of the chain $U(1)\subset U(2)\subset...$ of compact unitary groups. The group $U(\infty)$ operates on the space $H$ by conjugations,…

In this paper, we present a characterization of support functionals and smooth points in $L_{0}^{\Phi}$, the Musielak-Orlicz space equipped with the Orlicz norm. As a result, criterion for the smoothness of $L_{0}^{\Phi}$ is also obtained.…

In this paper, we deal with the family of Steklov sampling operators in the general setting of Orlicz spaces. The main result of the paper is a modular convergence theorem established following a density approach. To do this, a Luxemburg…

The Kardar-Parisi-Zhang (KPZ) equation on the real line is well-known to admit Brownian motion with a linear drift as a stationary distribution (modulo additive constants). We show that these solutions are attractive, a result known as a…

Nitsche's method is a standard device for weakly imposing Dirichlet boundary conditions, but for the stabilized nonsymmetric formulation the available $L^2$-error analysis for Poisson's equation still predicts a half-order loss, whereas…

Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…