Related papers: Automatic sequences as good weights for ergodic th…

In this work we prove the pointwise ergodic theorem for harmonic degree 1 cocycle of a measurable stationary action of Z^d on a probability space. In a precedent paper Boivin and Derriennic (1991) studied this theorem for not necessarily…

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…

This paper connects the classes of weighted alternating finite automata (WAFA), weighted finite tree automata (WFTA), and polynomial automata (PA). First, we investigate the use of trees in the run semantics for weighted alternating…

In this paper, we prove that the Hecke eigenvalue square for a holomorphic cusp form and the Piltz divisor functions are good weighting functions for the pointwise ergodic theorem. This partially solves problems suggested by Cuny and Weber.…

We prove that if $y=\sum_{n=0}^\infty{\bf a}(n)x^n\in\mathbb{F}_q[[x]]$ is an algebraic power series of degree $d$, height $h$, and genus $g$, then the sequence ${\bf a}$ is generated by an automaton with at most $q^{h+d+g-1}$ states, up to…

We study the ergodic properties of a class of controlled stochastic differential equations (SDEs) driven by $\alpha$-stable processes which arise as the limiting equations of multiclass queueing models in the Halfin-Whitt regime that have…

Given a finite alphabet $\mathbb{A}$ and a primitive substitution $\theta:\mathbb{A}\to\mathbb{A}^\lambda$ (of constant length $\lambda$), let $(X_\theta,S)$ denote the corresponding dynamical system, where $X_{\theta}$ is the closure of…

We show the $L^2$-convergence of continuous time ergodic averages of a product of functions evaluated at return times along polynomials. These averages are the continuous time version of the averages appearing in Furstenberg's proof of…

In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this…

We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…

Active learning of finite automata has been vigorously pursued for the purposes of analysis and explanation of black-box systems. In this paper, we study an L*-style learning algorithm for weighted automata over the max-plus semiring. The…

Let $(X,\mathcal{B},\mu)$ be a probability space and let $T_1,..., T_l$ be $l$ commuting invertible measure preserving transformations \linebreak of $X$. We show that if $T_1^{c_1} ... T_l^{c_l}$ is ergodic for each $(c_1,...,c_l)\neq…

We strengthen the maximal ergodic theorem for actions of groups of polynomial growth to a form involving jump quantity, which is the sharpest result among the family of variational or maximal ergodic theorems. As a consequence, we deduce in…

By definition, a map quasiperiodic on a set $X$ if the map is conjugate to a pure rotation. Suppose we have a trajectory $(x_n)$ that we suspect is quasiperiodic. How do we determine if it is? In this paper we show how to compute the…

It is shown that there exist a subsequence for which the multiple ergodic averages of commuting invertible measure preserving transformations of a Lebesgue probability space converge almost everywhere provided that the maps are weakly…

A theorem of Christol states that a power series over a finite field is algebraic over the polynomial ring if and only if its coefficients can be generated by a finite automaton. Using Christol's result, we prove that the same assertion…

We establish functional limit theorems for ergodic sums of observables with power singularities for expanding circle maps. In the regime where the observables have infinite variance, we show that when rescaled by $N^{1/s}(\ln N)^\alpha$,…

We present recent results about the asymptotic behavior of ergodic products of isometries of a metric space X. If we assume that the displacement is integrable, then either there is a sublinear diffusion or there is, for almost every…

The $n$th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of $n$ in a suitable numeration system. In this paper, instead of considering automatic sequences built on a numeration…

We give a new graph-theoretic proof of Cobham's Theorem which says that the support of an automatic sequence is either sparse or grows at least like $N^\alpha$ for some $\alpha > 0$. The proof uses the notions of tied vertices and cycle…