Related papers: Recurrence for stationary group actions

We prove a multiple recurrence result for arbitrary measure-preserving transformations along polynomials in two variables of the form $m+p_i(n)$, with rationally independent $p_i$'s with zero constant term. This is in contrast to the single…

We give a criterion to determine the large deviation rate functions for abstract dynamical systems on towers. As an application of this criterion we show the level 2 large deviation principle for some class of smooth interval maps with…

We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the…

We discuss selected topics of current research interest in the theory of dynamical systems, with emphasis on dimension theory, multifractal analysis, and quantitative recurrence. The topics include the quantitative versus the qualitative…

We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…

We extend previous results on noncommutative recurrence in unital *-algebras over the integers, to the case where one works over locally compact Hausdorff groups. We derive a generalization of Khintchine's recurrence theorem, as well as a…

We consider a natural class of reaction networks which consist of reactions where either two species can inactivate each other (i.e., sequestration), or some species can be transformed into another (i.e., transmutation), in a way that gives…

We investigate quantitative recurrence in systems having an infinite measure. We extend the Ornstein-Weiss theorem for a general class of infinite systems estimating return time in decreasing sequences of cylinders. Then we restrict to a…

We study a nonconventional ergodic average for asymptotically abelian weakly mixing C*-dynamical systems, related to a second iteration of Khintchine's recurrence theorem obtained by Bergelson in the measure theoretic case. A noncommutative…

We continue development of the theory of Markov systems initiated in \cite{Wer1}. In this paper, we introduce fundamental Markov systems associated with random dynamical systems and show that the proof of the uniqueness and empiricalness of…

We state and prove a theorem on the partitioning of a randomly selected large population into stationary and non-stationary components by using a property of stationary population identity. Applications of this theorem for practical…

A well-known generalisation of positional numeration systems is the case where the base is the residue class of $x$ modulo a given polynomial $f(x)$ with coefficients in (for example) the integers, and where we try to construct finite…

We present manifestly reparametrization invariant action for theory of gravity with dynamical determinant of metric. We show that it is similar to a reparametrization invariant action for unimodular gravity. We determine canonical form of…

A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…

Let $\mu$ and $\nu$ be probability measures on a group \Gamma and let G_\mu and G_\nu denote Green's function with respect to \mu and \nu . The group \Gamma is said to admit instability of Green's function if there are symmetric, finitely…

We present some necessary and/or sufficient conditions for the positivity problem of three-term recurrence sequences. As applications we show the positivity of diagonal Taylor coefficients of some rational functions in a unified approach.…

In this article we survey some of the recent developments in the structure theory of set addition.

We present a probabilistic generative model for inferring a description of coordinated, recursively structured group activities at multiple levels of temporal granularity based on observations of individuals' trajectories. The model…

For a class of stationary regularly varying and weakly dependent time series, we prove the so-called complete convergence result for the corresponding space-time point processes. As an application of our main theorem, we give a simple proof…

This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent…