Related papers: Ergodicity of a collective random walk on a circle
Entropic forces result from an increase of the entropy of a thermodynamical physical system. It has been proposed that gravity is such a phenomenon and many articles have appeared on the literature concerning this problem. Loop quantum…
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical…
We derive a perturbation expansion for general self-interacting random walks, where steps are made on the basis of the history of the path. Examples of models where this expansion applies are reinforced random walk, excited random walk, the…
We derive the first two moments of generic positive stochastic functionals in terms of the one- and two-time probability density functions of the underlying random walk, and we prove ergodicity of observables in stationary random walks.…
We study dynamic random conductance models on $\mathbb{Z}^2$ in which the environment evolves as a reversible Markov process that is stationary under space-time shifts. We prove under a second moment assumption that two conditionally…
A random walk on a $N$-dimensional hypercube is a discrete time stochastic process whose state space is the set $\{-1,+1\}^{N}$, which has uniform probability of reaching any neighbour state, and probability zero of reaching a non-neighbour…
We consider a one-dimensional simple symmetric exclusion process in equilibrium, constituting a dynamic random environment for a nearest-neighbor random walk that on occupied/vacant sites has two different local drifts to the right. We…
Aims. The random walk of energetic charged particles in turbulent magnetic fields is investigated. Special focus is placed on transport across the mean magnetic field, which had been found to be subdiffusive on many occasions. Therefore, a…
Given the increments of a simple symmetric random walk $(X_n)_{n\ge0}$, we characterize all possible ways of recycling these increments into a simple symmetric random walk $(Y_n)_{n\ge0}$ adapted to the filtration of $(X_n)_{n\ge0}$. We…
Given a random walk a method is presented to produce a matrix of transition probabilities that is consistent with that random walk. The method is a kind of reverse application of the usual ergodicity and is tested by using a transition…
A spider consists of several, say $N$, particles. Particles can jump independently according to a random walk if the movement does not violate some given restriction rules. If the movement violates a rule it is not carried out. We consider…
It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuous-time…
A number of papers have examined various aspects of "random random" walks on finite groups; the purpose of this article is to provide a survey of this work and to show, bring together, and discuss some of the arguments and results in this…
In this note we study dynamical random walks (DRW) with internal states. We consider a particle which performs a dynamical random walk on $\mathbb{Z}$ and whose local dynamics is given by expanding maps. We provide sufficient conditions for…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Understanding the organization of collective motion in biological systems is an ongoing challenge. In this Paper we consider a minimal model of self-propelled particles with variable speed. Inspired by experimental data from schooling fish,…
A one dimensional classically chaotic spin chain with asymmetric coupling and two different inter-spin interactions, nearest neighbors and all-to-all, has been considered. Depending on the interaction range, dynamical properties, as…
We show that in classical spin systems the precise nature of the late-time hydrodynamic tails of the autocorrelation functions of a generic observable is determined by (i) the dynamical critical exponent and (ii) the equilibrium…
Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic…
The emergence of collective motion, also known as flocking or swarming, in groups of moving individuals who orient themselves using only information from their neighbors is a very general phenomenon that is manifested at multiple spatial…