Related papers: Generalized Dobrushin Ergodicity Coefficient and U…

In this paper, we establish moment and Bernstein-type inequalities for additive functionals of geometrically ergodic Markov chains. These inequalities extend the corresponding inequalities for independent random variables. Our conditions…

The main aim of this work is to establish an averaging principle for a wide class of interacting particle systems in the continuum. This principle is an important step in the analysis of Markov evolutions and is usually applied for the…

The main goal of the paper is to prove convergence in norm and pointwise almost everywhere on $L^p$, $p\in (1,\infty)$, for certain multiparameter polynomial ergodic averages in the spirit of Dunford and Zygmund for continuous flows. We…

In this paper, we investigate the ergodicity in total variation of the process $X_t$ related to some integro-differential operator with unbounded coefficients and describe the speed of convergence to the respective invariant measure. Some…

Let $U$ be a unitary operator acting on the Hilbert space $H$, $\a:\{1,..., 2k\}\mapsto\{1,..., k\}$ a pair--partition, and finally $A_{1},...,A_{2k-1}\in B(H)$. We show that the ergodic average $$…

This paper is a physicist's review of the major conceptual issues concerning the problem of spectral universality in quantum systems. Here we present a unified, graph-based view of all archetypical models of such universality (billiards,…

We introduce an statistical mechanical formalism for the study of discrete-time stochastic processes with which we prove: (i) General properties of extremal chains, including triviality on the tail $\sigma$-algebra, short-range…

In the present paper we investigate $L_0$-valued states and Markov operators on $ C^*$-algebras over $L_0$. In particular, we give representations for $L_0$-valued state and Markov operators on $ C^*$ algebras over $L_0$, respectively, as…

We study Markovian random products on a large class of "m-dimensional" connected compact metric spaces (including products of closed intervals and trees). We introduce a splitting condition, generalizing the classical one by Dubins and…

A formula for the transition density of a Markov process defined by an infinite-dimensional stochastic equation is given in terms of the Ornstein--Uhlenbeck bridge and a useful lower estimate on the density is provided. As a consequence,…

We prove ergodicity for random dynamics satisfying some expansion and irreducibility conditions. As a particular application, we show that if $R_1,R_2\in \mathrm{SO}(d+1)$, $d\ge 2$, generate a dense subgroup, then the random dynamics of…

A concurrent system is defined as a monoid action of a trace monoid on a finite set of states. Concurrent systems represent state models where the state is distributed and where state changes are local. Starting from a spectral property on…

Ergodicity of random dynamical systems with a periodic measure is obtained on a Polish space. In the Markovian case, the idea of Poincar\'e sections is introduced. It is proved that if the periodic measure is PS-ergodic, then it is ergodic.…

We give a bound on the mixing time of a uniformly ergodic, reversible Markov chain in terms of the spectral radius of the transition operator. This bound has been established previously in finite state spaces, and is widely believed to hold…

In this review-type paper written at the occasion of the Oberwolfach workshop {\em One-sided vs. Two-sided stochastic processes} (february 22-29, 2020), we discuss and compare Markov properties and generalisations thereof in more…

We characterize the geometrically doubling condition of a metric space in terms of the uniform $L^1$-boundedness of superaveraging operators, where uniform refers to the existence of bounds independent of the measure being considered.

Consider a Markov process $\{\Phi(t) : t\geq 0\}$ evolving on a Polish space ${\sf X}$. A version of the $f$-Norm Ergodic Theorem is obtained: Suppose that the process is $\psi$-irreducible and aperiodic. For a given function $f\colon{\sf…

The main goal of this note is to show that (not necessarily holomorphic) multipliers of a wide class of normed spaces of continuous functions over a connected Hausdorff topological space cannot attain their multiplier norms, unless they are…

This paper consists of four parts. In the first part, we explain what eigenvalues we are interested in and show the difficulties of the study on the first (non-trivial) eigenvalue through examples. In the second part, we present some (dual)…

In this paper we study the ergodicity and the related semigroup property for a class of symmetric Markov jump processes associated with time changed symmetric $\alpha$-stable processes. For this purpose, explicit and sharp criteria for…