Related papers: Alsed\`a-Misiurewicz systems with place-dependent …
We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results established in [2]. First of all the random walk is transient in dimension at least three. Focusing on dimension two,…
This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…
Markov chains in random environments (MCREs) have recently attracted renewed interest, as these processes naturally arise in many applications, such as econometrics and machine learning. Although specific asymptotic results, such as the law…
Piecewise Deterministic Markov Processes (PDMPs) are studied in a general framework. First, different constructions are proven to be equivalent. Second, we introduce a coupling between two PDMPs following the same differential flow which…
We introduce the concept of a Markov influence system (MIS) and analyze its dynamics. An MIS models a random walk in a graph whose edges and transition probabilities change endogenously as a function of the current distribution. This…
We study symmetric random walks on finitely generated groups of orientation-preserving homeomorphisms of the real line. We establish an oscillation property for the induced Markov chain on the line that implies a weak form of recurrence.…
We study the problem of generating connected random graphs with no self-loops or multiple edges and that, in addition, have a given degree sequence. The generation method we focus on is the edge-switching Markov-chain method, whose…
We consider Markov chains with random transition probabilities which, moreover, fluctuate randomly with time. We describe such a system by a product of stochastic matrices, $U(t)=M_t\cdots M_1$, with the factors $M_i$ drawn independently…
In this paper, we consider linear switched systems $\dot x(t)=A_{u(t)} x(t)$, $x\in\R^n$, $u\in U$, and the problem of asymptotic stability for arbitrary switching functions, uniform with respect to switching ({\bf UAS} for short). We first…
We explain the relation between certain random tiling models and interacting particle systems belonging to the anisotropic KPZ (Kardar-Parisi-Zhang) universality class in 2+1-dimensions. The link between these two \emph{a priori} disjoint…
The limiting probability distribution is one of the key characteristics of a Markov chain since it shows its long-term behavior. In this paper, for a higher order Markov chain, we establish some properties related to its exact limiting…
We study a generalized notion of a homogeneous skew-product extension of a probability-preserving system in which the homogeneous space fibres are allowed to vary over the ergodic decomposition of the base. The construction of such…
We analyze the asymptotic behavior of sequences of random variables defined by an initial condition, a stationary and ergodic sequence of random matrices, and an induction formula involving multiplication is the so-called max-plus algebra.…
We consider finite-state time-nonhomogeneous Markov chains where the probability of moving from state $i$ to state $j\neq i$ at time $n$ is $G(i,j)/n^\zeta$ for a ``generator'' matrix $G$ and strength parameter $\zeta>0$. In these chains,…
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 consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a mean vector field which induces the coupling between the…
We introduce a variant of the Erd\"os--R\'enyi random graph where the number of vertices is random and follows a Poisson law. A very simple Markov property of the model entails that the Lukasiewicz exploration is made of…
Motivated by theoretical analyses of spatially localized structures with arbitrarily long periodic plateaus, we provide a framework of assumptions that simplifies their analysis and leads to a topological criterion for when localized…
Motivated by the study of the time evolution of random dynamical systems arising in a vast variety of domains --- ranging from physics to ecology ---, we establish conditions for the occurrence of a non-trivial asymptotic behaviour for…
In many dynamical systems in nature, the law of the dynamics changes along with the temporal evolution of the system. These changes are often associated with the occurrence of certain events. The timing of occurrence of these events…