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The processes described in the title always have reversible stationary distributions. In this paper, we give sufficient conditions for the existence of, and for the nonexistence of, nonreversible stationary distributions. In the case of an…

Probability · Mathematics 2009-11-13 Lincoln Chayes , Thomas M. Liggett

There exist very few results on mixing for non-stationary processes. However, mixing is often required in statistical inference for non-stationary processes such as time-varying ARCH (tvARCH) models. In this paper, bounds for the mixing…

Statistics Theory · Mathematics 2011-02-11 Piotr Fryzlewicz , Suhasini Subba Rao

In computational models of particle packings with periodic boundary conditions, it is assumed that the packing is attached to exact copies of itself in all possible directions. The periodicity of the boundary then requires that all of the…

Soft Condensed Matter · Physics 2022-09-07 R. Cameron Dennis , Varda F. Hagh , Eric I. Corwin

We study mixing properties of generalized $T, T^{-1}$ transformation. We discuss two mixing mechanisms. In the case the fiber dynamics is mixing, it is sufficient that the driving cocycle is small with small probability. In the case the…

Dynamical Systems · Mathematics 2020-12-01 Dmitry Dolgopyat , Changguang Dong , Adam Kanigowski , Peter Nándori

We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is…

Probability · Mathematics 2024-12-23 Ion Grama , Émile Le Page , Marc Peigné

We consider Markov chains on general state spaces in stationary random environment which are defined by a random mapping that is contractive up to a bounded perturbation. We prove their convergence to a limiting law, providing convergence…

Probability · Mathematics 2025-12-18 Attila Lovas , Miklós Rásonyi , Lionel Truquet

We introduce and study two properties of dynamical systems: topologically transitive and topologically mixing under the set-valued setting. We prove some implications of these two topological properties for set-valued functions and…

Dynamical Systems · Mathematics 2019-03-29 Wong Koon Sang , Zabidin Salleh

We derive rates of convergence for the mixing of operators under infinitely divisible measures in the framework of linear dynamics on Banach spaces. Our approach is based on the characterization of mixing in terms of codifference…

Probability · Mathematics 2025-11-12 Camille Mau , Nicolas Privault

We investigate weak mixing for some classes of interval translation mappings. We give two distinct proofs that a typical Bruin-Troubetzkoy interval translation mapping is weakly mixing. Moreover, we show that the second approach extends to…

Dynamical Systems · Mathematics 2026-03-23 Mauro Artigiani , Artur Avila , Sébastien Ferenczi , Pascal Hubert , Alexandra Skripchenko

We exhibit rationally ergodic, weakly mixing measure preserving transformations which are not subsequence rationally weakly mixing and give a condition for smoothness of renewal sequences.

Dynamical Systems · Mathematics 2016-08-03 J. Aaronson

The paper considers two main results. First one is the uniform bound for strong mixing coefficient of ARCH sequence. Second is the bound for maximum of residual empirical process in the same model. We illustrate their usefulness by proving…

Statistics Theory · Mathematics 2007-06-13 Alexey Sorokin

We present a sufficient condition that a pseudointegrable system has weak mixing property. The result is derived from Veech's weak mixing theorem for interval exhange [Veech, W.A. Amer.J.Math. {\bf 106}, 1331 (1984)]. We also present an…

Dynamical Systems · Mathematics 2007-05-23 Minoru Ogawa

We consider random fields that can be represented as integrals of deterministic functions with respect to infinitely divisible random measures and show that these random fields are infinitely divisible.

Probability · Mathematics 2010-08-13 Wolfgang Karcher , Hans-Peter Scheffler , Evgeny Spodarev

An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…

Other Statistics · Statistics 2018-03-05 Hien D. Nguyen , Geoffrey J. McLachlan

Let $\{X_{\mathbf{n}} : \mathbf{n}\in\mathbb{Z}^d\}$ be a weakly dependent stationary field with maxima $M_{A} := \sup\{X_{\mathbf{i}} : \mathbf{i}\in A\}$ for finite $A\subset\mathbb{Z}^d$ and $M_{\mathbf{n}} := \sup\{X_{\mathbf{i}} :…

Probability · Mathematics 2019-08-20 Natalia Soja-Kukieła

We introduce a variation of strong stationary times for random walks on the symmetric group. Rather than proceed in the usual fashion of accumulating larger and larger blocks of cards which may be in any order, we wait for pairs of cards to…

Probability · Mathematics 2019-10-08 Graham White

This paper establishes the asymptotic normality of frequency polygons in the context of stationary strongly mixing random fields indexed by $\Z^d$. Our method allows us to consider only minimal conditions on the width bins and provides a…

Statistics Theory · Mathematics 2013-07-29 Mohamed El Machkouri

We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include…

Dynamical Systems · Mathematics 2014-04-11 Ian Melbourne , Dalia Terhesiu

We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…

Probability · Mathematics 2019-03-05 Thomas Sauerwald , Luca Zanetti

We prove results on mixing and mixing rates for toral extensions of nonuniformly expanding maps with subexponential decay of correlations. Both the finite and infinite measure settings are considered. Under a Dolgopyat-type condition on…

Dynamical Systems · Mathematics 2018-11-02 Ian Melbourne , Dalia Terhesiu