Related papers: Semi-deterministic processes with applications in …
We study a system of $N$ interacting particles on $\bf{Z}$. The stochastic dynamics consists of two components: a free motion of each particle (independent random walks) and a pair-wise interaction between particles. The interaction belongs…
We study ergodic properties of one-dimensional Brownian motion with resetting. Using generic classes of statistics of times between resets, we find respectively for thin/fat tailed distributions, the normalized/non-normalised invariant…
We consider a classic two-state switching diffusion model from a single-particle tracking perspective. The mean and the variance of the time-averaged mean square displacement (TAMSD) are computed exactly. When the measurement time (i.e.,…
We study a phenomenological model for the continuous double auction, equivalent to two independent $M/M/1$ queues. The continuous double auction defines a continuous-time random walk for trade prices. The conditions for ergodicity of the…
A Markov chain is geometrically ergodic if it converges to its in- variant distribution at a geometric rate in total variation norm. We study geo- metric ergodicity of deterministic and random scan versions of the two-variable Gibbs…
We introduce a class of discrete random walk model driven by global memory effects. At any time the right-left transitions depend on the whole previous history of the walker, being defined by an urn-like memory mechanism. The characteristic…
We provide a probabilistic analysis of the banker algorithm when transition probabilities may depend on time and space. The transition probabilities evolve, as time goes by, along the trajectory of an ergodic Markovian environment, whereas…
In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…
We introduce a class of random mechanical systems called random billiards to study the problem of quantifying the irreversibility of nonequilibrium macroscopic systems. In a random billiard model, a point particle evolves by free motion…
This paper is devoted to the study of a stochastic process obtained by random switching between a finite collection of vector fields. Such processes have recently been the focus of much attention in the case where the switching times are…
We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a…
A one-dimensional confined Nonlinear Random Walk is a tuple of $N$ diffeomorphisms of the unit interval driven by a probabilistic Markov chain. For generic such walks, we obtain a geometric characterization of their ergodic stationary…
In this paper we study the ergodicity and the related semigroup property for a class of symmetric Markov jump processes associated with time changed symmetric $\alpha$-stable processes. For this purpose, explicit and sharp criteria for…
The ergodic decomposition theorem is a cornerstone result of dynamical systems and ergodic theory. It states that every invariant measure on a dynamical system is a mixture of ergodic ones. Here we formulate and prove the theorem in terms…
We consider stationary stochastic dynamical systems evolving on a compact metric space, by perturbing a deterministic dynamics with a random noise, added according to an arbitrary probabilistic distribution. We prove the maximal and…
Motivated by a model presented by S. Gudder, we study a quantum generalization of Markov chains and discuss the relation between these maps and open quantum random walks, a class of quantum channels described by S. Attal et al. We consider…
This paper is concerned with ergodic properties of inhomogeneous Markov processes. Since the transition probabilities depend on initial times, the existing methods to obtain invariant measures for homogeneous Markov processes are not…
The random walk with hyperbolic probabilities that we are introducing is an example of stochastic diffusion in a one-dimensional heterogeneous media. Although driven by site-dependent one-step transition probabilities, the process retains…
We consider the billiard dynamics in a non-compact set of R^d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy.…
Subshifts of deterministic substitutions are ubiquitous objects in dynamical systems and aperiodic order (the mathematical theory of quasicrystals). Two of their most striking features are that they have low complexity (zero topological…