Related papers: Stationary Measures for Random Walks in a Random E…
We present a novel quasi-Monte Carlo mechanism to improve graph-based sampling, coined repelling random walks. By inducing correlations between the trajectories of an interacting ensemble such that their marginal transition probabilities…
Kemeny's constant measures how fast a random walker moves around in a graph. Expressions for Kemeny's constant can be quite involved, and for this reason, many lines of research focus on graphs with structure that makes them amenable to…
We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure.
A L\'evy random medium, in a given space, is a random point process where the distances between points, a.k.a. targets, are long-tailed. Random walks visiting the targets of a L\'evy random medium have been used to model many (physical,…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where…
We give the random environment version of Mogul'ski\v{\i} estimation in quenched sense.Assume that $\{\mu\}_{n\in\bfN}$ (called environment) is a sequence of i.i.d. random probability measures on $\bfR.$~ Let $\{X_n\}_{n\in\bfN}$ be a…
We study the behavior of Random Walk in Random Environment (RWRE) on trees in the critical case left open in previous work. Representing the random walk by an electrical network, we assume that the ratios of resistances of neighboring edges…
The first motivation of this paper is to study stationarity and ergodic properties for a general class of time series models defined conditional on an exogenous covariates process. The dynamic of these models is given by an autoregressive…
Quantum trajectories are Markov processes modeling the evolution of a quantum system subjected to repeated independent measurements. Inspired by the theory of random products of matrices, it has been shown that these Markov processes admit…
Certain continuous-time quantum walks can be viewed as scattering processes. These processes can perform quantum computations, but it is challenging to design graphs with desired scattering behavior. In this paper, we study and construct…
We introduce the notion of a "random basic walk" on an infinite graph, give numerous examples, list potential applications, and provide detailed comparisons between the random basic walk and existing generalizations of simple random walks.…
We consider impulsive dynamical systems defined on compact metric spaces and their respective impulsive semiflows. We establish sufficient conditions for the existence of probability measures which are invariant by such impulsive semiflows.…
We consider the random walk in an \emph{i.i.d.} random environment on the infinite $d$-regular tree for $d \geq 3$. We consider the tree as a Cayley graph of free product of finitely many copies of $\Zbold$ and $\Zbold_2$ and define the…
The conditions $(T)_\gamma,$ $\gamma \in (0,1),$ which have been introduced by Sznitman in 2002, have had a significant impact on research in random walk in random environment. Among others, these conditions entail a ballistic behaviour as…
The propagation of an initially localized perturbation via an interacting many-particle Hamiltonian dynamics is investigated. We argue that the propagation of the perturbation can be captured by the use of a continuous-time random walk…
Random walks on the circle group $\mathbb{R}/\mathbb{Z}$ whose elementary steps are lattice variables with span $\alpha \not\in \mathbb{Q}$ or $p/q \in \mathbb{Q}$ taken mod $\mathbb{Z}$ exhibit delicate behavior. In the rational case we…
This paper presents a nonlinear approach to measurements a general framework for dealing with variations of environmental conditions. My method may prove promising to extensions beyond classical physics, economics, and other sciences. I…
We study dynamical systems acting on the path space of a stationary (non-simple) Bratteli diagram. For such systems we explicitly describe all ergodic probability measures invariant with respect to the tail equivalence relation (or the…
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…