Related papers: Dynamical properties of random walks
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
This paper studies the on- and off-diagonal upper estimate and the two-sided transition probability estimate of random walks on weighted graphs.
We make a connection between the continuous time and lazy discrete time Markov chains through the comparison of cutoffs and mixing time in total variation distance. For illustration, we consider finite birth and death chains and provide a…
The large deviation theory has recently been applied to open quantum systems to uncover dynamical crossovers in the space of quantum trajectories associated to Markovian evolutions. Such dynamical crossovers are characterized by qualitative…
We study Markov chains on $\mathbb Z^m$, $m\geq 2$, that behave like a standard symmetric random walk outside of the hyperplane (membrane) $H=\{0\}\times \mathbb Z^{m-1}$. The transition probabilities on the membrane $H$ are periodic and…
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…
Simple random walks on various types of partially horizontally oriented regular lattices are considered. The horizontal orientations of the lattices can be of various types (deterministic or random) and depending on the nature of the…
We investigate analytically and numerically the statistical properties of a random walk model with delayed transition probability dependence (delayed random walk). The characteristic feature of such a model is the oscillatory behavior of…
The work treats systems combining slow and fast motions depending on each other where fast motions are perturbations of families of either dynamical systems or Markov processes with freezed slow variable. In the first case we consider…
Linear chains of quantum scatterers are studied in the process of lengthening, which is treated and analysed as a discrete dynamical system defined over the manifold of scattering matrices. Elementary properties of such dynamics relate the…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
We study the spectral theory of a reversible Markov chain associated to a hypoelliptic random walk on a manifold M. This random walk depends on a parameter h which is roughly the size of each step of the walk. We prove uniform bounds with…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…
This paper introduces the Attracting Random Walks model, which describes the dynamics of a system of particles on a graph with $n$ vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with…
This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…
We examine dynamic structure factors of spin-1/2 chains with nearest-neighbor interactions of XX and Dzyaloshinskii-Moriya type, and with periodic and random changes in the sign of these interactions. This special kind of inhomogeneity can…
We consider the problem of stochastic flow of multiple particles traveling on a closed loop, with a constraint that particles move without passing. We use a Markov chain description that reduces the problem to a generalized random walk on a…
In [4], we examined the use of coupling to obtain bounds on the mixing time of statistics on Markov chains. In the present paper, we consider the same general problem, but using strong stationary times rather than coupling. We discuss…
We introduce and study the topological concepts of chain transitivity, mixing and chain mixing property for dynamical systems induced by uniform hyperspaces. These notions generalize the relevant concepts for metric spaces.
A discrete-time Markov chain can be transformed into a new Markov chain by looking at its states along iterations of an almost surely finite stopping time. By the optional stopping theorem, any bounded harmonic function with respect to the…