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We introduce a class of nearest-neighbor integer random walks in random and non-random media, which includes excited random walks considered in the literature. At each site the random walker has a drift to the right, the strength of which…

The transition probability for a one-dimensional discrete symmetric random walk under a reflecting barrier was once given by the method of images. [S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).] However, several inconsistencies have been…

There exist a large literature on the application of $q$-statistics to the out-of-equilibrium non-ergodic systems in which some degree of strong correlations exists. Here we study the distribution of first return times to zero, $P_R(0,t)$,…

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 introduce a continuous-time random walk model on an infinite multilayer structure inspired by transportation networks. Each layer is a copy of $\mathbb{R}^d$, indexed by a non-negative integer. A walker moves within a layer by means of…

We study the winding behavior of random walks on two oriented square lattices. One common feature of these walks is that they are bound to revolve clockwise. We also obtain quantitative results of transience/recurrence for each walk.

Negative refraction is a peculiar wave propagation phenomenon that occurs when a wave crosses a boundary between a regular medium and a medium with both constitutive parameters negative at the given frequency. The phase and group velocities…

We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…

This paper is focused on the statistical analysis of data consisting of a collection of multiple series of probability measures that are indexed by distinct time instants and supported over a bounded interval of the real line. By modeling…

We establish an invariance principle for a one-dimensional random walk in a dynamical random environment given by a speed-change exclusion process. The jump probabilities of the walk depend on the configuration of the exclusion in a finite…

We consider a Markov-modulated Brownian motion reflected to stay in a strip [0,B]. The stationary distribution of this process is known to have a simple form under some assumptions. We provide a short probabilistic argument leading to this…

We consider random walks in which the walk originates in one set of nodes and then continues until it reaches one or more nodes in a target set. The time required for the walk to reach the target set is of interest in understanding the…

The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…

We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to…

We study a simple run-and-tumble random walk whose switching frequency from run mode to tumble mode and the reverse depend on a stochastic signal. We consider a particularly sharp, step-like dependence, where the run to tumble switching…

We propose the concepts of distributed robustness and r-robustness, well adapted to functional genetics. Then we discuss the robustness of the relaxation time using a chemical reaction description of genetic and signalling networks. First,…

We consider a system of independent one-dimensional random walks in a common random environment under the condition that the random walks are transient with positive speed $v_P$. We give upper bounds on the quenched probability that at…

We consider the dynamics of lattice random walks with resetting. The walker moving randomly on a lattice of arbitrary dimensions resets at every time step to a given site with a constant probability $r$. We construct a discrete renewal…

We introduce and study a non-oriented first passage percolation model having a property of statistical invariance by time reversal. This model is defined in a graph having directed edges and the passage times associated with each set of…

We introduce and analyze a one-dimensional quantum walk with two time-independent rotations on the coin. We study the influence on the property of quantum walk due to the second rotation on the coin. Based on the asymptotic solution in the…