Related papers: The *-Edge-Reinforced Random Walk

We propose a model of random walks on weighted graphs where the weights are interval valued, and connect it to reversible imprecise Markov chains. While the theory of imprecise Markov chains is now well established, this is a first attempt…

We show that the "twisted" planar random walk - which results by summing up stationary increments rotated by multiples of a fixed angle - is recurrent under diverse assumptions on the increment process. For example, if the increment process…

This paper concerns the Vertex reinforced jump process (VRJP), the Edge reinforced random walk (ERRW) and their link with a random Schr\"odinger operator. On infinite graphs, we define a 1-dependent random potential $\beta$ extending that…

We review various features of the statistics of random paths on graphs. The relationship between path statistics and Quantum Mechanics (QM) leads to two canonical ways of defining random walk on a graph, which have different statistics and…

One class of random walks with infinite memory, so called elephant random walks, are simple models describing anomalous diffusion. We present a surprising connection between these models and bond percolation on random recursive trees. We…

The iterated random walk is a random process in which a random walker moves on a one-dimensional random walk which is itself taking place on a one-dimensional random walk, and so on. This process is investigated in the continuum limit using…

A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…

We study random walks on the giant component of the Erd\H{o}s-R\'enyi random graph ${\cal G}(n,p)$ where $p=\lambda/n$ for $\lambda>1$ fixed. The mixing time from a worst starting point was shown by Fountoulakis and Reed, and independently…

We use Kashiwara crystal basis theory to associate a random walk W to each irreducible representation V of a simple Lie algebra. This is achieved by endowing the crystal attached to V with a (possibly non uniform) probability distribution…

We consider a special case of random walk in random environment (RWRE) on Z^d where the environment is periodic (RWPE). Under natural conditions, we show that law of large numbers and central limit theorem holds. In the ballistic nearest…

We consider a continuous-time random walk which is defined as an interpolation of a random walk on a point process on the real line. The distances between neighboring points of the point process are i.i.d. random variables in the normal…

In probability theory, reinforced walks are random walks on a lattice (or more generally a graph) that preferentially revisit neighboring `locations' (sites or bonds) that have been visited before. In this paper, we consider walks with…

We study properties of a non-Markovian random walk $X^{(n)}_l$, $l =0,1,2, >...,n$, evolving in discrete time $l$ on a one-dimensional lattice of integers, whose moves to the right or to the left are prescribed by the…

We give evidence that the functional renormalization group (FRG), developed to study disordered systems, may provide a field theoretic description for the loop-erased random walk (LERW), allowing to compute its fractal dimension in a…

A random walk with counterbalanced steps is a process of partial sums $\check S(n)=\check X_1+ \cdots + \check X_n$ whose steps $\check X_n$ are given recursively as follows. For each $n\geq 2$, with a fixed probability $p$, $\check X_n$ is…

We consider a certain sequence of random walks. The state space of the n-th random walk is the set of all strict partitions of n (that is, partitions without equal parts). We prove that, as n goes to infinity, these random walks converge to…

Very often when studying non-equilibrium systems one is interested in analysing dynamical behaviour that occurs with very low probability, so called rare events. In practice, since rare events are by definition atypical, they are often…

In this paper, we consider a spectral analysis of the Correlated Random Walk (CRW) on the path. We apply an analytical method for the Quantum Walk to CRW. For the isospectral coin cases, we obtain all of the eigenvalues and the…

We construct a two-dimensional counterexample of a random walk in random environment (RWRE). The environment is stationary, mixing and perturbative, and the corresponding RWRE has non-trivial probability to wander off to the upper right.…

In this article, we consider the speed of the random walks in a (uniformly elliptic and i.i.d.) random environment (RWRE) under perturbation. We obtain the derivative of the speed of the RWRE w.r.t. the perturbation, under the assumption…