Related papers: Deviation of ergodic averages for substitution dyn…
It is well-known that the dynamical spectrum of an ergodic measure dynamical system is related to the diffraction measure of a typical element of the system. This situation includes ergodic subshifts from symbolic dynamics as well as…
A pseudorandom point in an ergodic dynamical system over a computable metric space is a point which is computable but its dynamics has the same statistical behavior as a typical point of the system. It was proved in [Avigad et al. 2010,…
We give a general method of deriving statistical limit theorems, such as the central limit theorem and its functional version, in the setting of ergodic measure preserving transformations. This method is applicable in situations where the…
We introduce a variant of the asymmetric random average process with continuous state variables where the maximal transport is restricted by a cutoff. For periodic boundary conditions, we show the existence of a phase transition between a…
In this paper we are concerned with the study of additive ergodic averages in multiplicative systems and the investigation of the "pretentious" dynamical behaviour of these systems. We prove a mean ergodic theorem (Theorem A) that…
We study almost sure limiting behavior of extreme and intermediate order statistics arising from strictly stationary sequences. First, we provide sufficient dependence conditions under which these order statistics converges almost surely to…
We consider a control problem for a heterogeneous population composed of agents able to switch at any time between different options. The controller aims to maximize an average gain per time unit, supposing that the population is of…
If $\mathcal{A}$ is a finite set (alphabet), the shift dynamical system consists of the space $\mathcal{A}^{\mathbb{N}}$ of sequences with entries in $\mathcal{A}$, along with the left shift operator $S$. Closed $S$-invariant subsets are…
Given a positive increasing function $\varphi$, we show that for a full measure set of vectors $\alpha\in \mathbb{R}^d$, the maximal ergodic discrepancy of the $d$-linear form sequence $\left\{\sum_{1\le i\le d} k_i\alpha_i \mod…
In this paper, we are interested in the limit theorem question for sums of indicator functions. We show that in every aperiodic dynamical system, for every increasing sequence $(a_n)_{n\in\N}\subset\R_+$ such that $a_n\nearrow\infty$ and…
In ergodic physical systems, time-averaged quantities converge (for large times) to their ensemble-averaged values. Large deviation theory describes rare events where these time averages differ significantly from the corresponding ensemble…
A classical fact in ergodic theory is that ergodicity is equivalent to almost everywhere divergence of ergodic sums of all nonnegative integrable functions which are not identically zero. We show two methods, one in the measure preserving…
We extend the theory of ergodic optimization and maximizing measures to the non-commutative field of C*-dynamical systems. We then provide a result linking the ergodic optimizations of elements of a C*-dynamical system to the convergence of…
Given pseudo-random binary sequence of length $L$, assuming it consists of $k$ sub-sequences of length $N$. We estimate how $k$ scales with growing $N$ to obtain a {\it limiting} ergodic behaviour, to fulfill the basic definition of…
Experiments on particles' motion in living cells show that it is often subdiffusive. This subdiffusion may be due to trapping, percolation-like structures, or viscoelatic behavior of the medium. While the models based on trapping (leading…
In the framework of statistical mechanics the properties of macroscopic systems are deduced starting from the laws of their microscopic dynamics. One of the key assumptions in this procedure is the ergodic property, namely the equivalence…
In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable- and…
We consider Bourgain's ergodic theorem regarding arithmetic averages in the cases where quantitative mixing is present in the dynamical system. Focusing on the case of the horocyclic flow, those estimates allows us to bound from above the…
We present a new proof of an Ergodic theorem for Wide-Sense Stationary Random Processes added with a new canonical sampling theorem of mine for finite time duration signals in the frequency domain (periodograms) which is free from the…
The classical Birkhoff ergodic theorem in its most popular version says that the time average along a single typical trajectory of a dynamical system is equal to the space average with respect to the ergodic invariant distribution. This…