Related papers: On two duality properties of random walks in rando…
Based on studies on four specific networks, we conjecture a general relation between the walk dimensions $d_{w}$ of discrete-time random walks and quantum walks with the (self-inverse) Grover coin. In each case, we find that $d_{w}$ of the…
We consider a random walk on Z^d in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from x to nearest neighbor x+e is the same as to nearest neighbor x-e. Assuming that the environment is…
We consider two independent quantum walks on separate lines augmented by partial or full swapping of coins after each step. For classical random walks, swapping or not swapping coins makes little difference to the random walk…
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…
We show that the coined quantum walk on a line can be understood as an interference phenomenon, can be classically implemented, and indeed already has been. The walk is essentially two independent walks associated with the different coin…
We introduce a family of two-dimensional reflected random walks in the positive quadrant and study their Martin boundary. While the minimal boundary is systematically equal to a union of two points, the full Martin boundary exhibits an…
We study an extended dynamical system on the non-negative real line with piecewise linear non-uniformly expanding local dynamics. With a uniformly distributed initial state, the distribution of successive states coincides with that of a…
We consider a random walker whose motion is tethered around a focal point. We use two models that exhibit the same spatial dependence in the steady state but widely different dynamics. In one case, the walker is subject to a deterministic…
We study the motion of two non-interacting quantum particles performing a random walk on a line and analyze the probability that the two particles are detected at a particular position after a certain number of steps (meeting problem). The…
We study a class of non-reversible, continuous-time random walks in random environments on $\mathbb{Z}^d$ that admit a cycle representation with finite cycle length. The law of the transition rates, taking values in $[0, \infty)$, is…
The paper deals with the asymptotic properties of a symmetric random walk in a high contrast periodic medium in $\mathbb Z^d$, $d\geq 1$. We show that under proper diffusive scaling the random walk exhibits a non-standard limit behaviour.…
Consider a simple random walk on the integers with the following transition mechanism. At each site $x$, the probability of jumping to the right is $\omega(x)\in[\frac12,1)$, until the first time the process jumps to the left from site $x$,…
We consider the two-dimensional simple random walk conditioned on never hitting the origin. This process is a Markov chain, namely it is the Doob $h$-transform of the simple random walk with respect to the potential kernel. It is known to…
In this paper we consider the one-dimensional quantum random walk X^{varphi} _n at time n starting from initial qubit state varphi determined by 2 times 2 unitary matrix U. We give a combinatorial expression for the characteristic function…
In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5-25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561-575]. A random walk performs a motion in an i.i.d. environment and observes an…
The paper is devoted to an invariance principle for Kemperman's model of oscillating random walk on $\mathbb{Z}$. This result appears as an extension of the invariance principal theorem for classical random walks on $\mathbb{Z}$ or…
In this paper, we propose and analyze a novel one-dimensional inhomogeneous random walk model that combines spatial decay of transition probabilities with a temporal renewal structure for each excursion. In this model, the probability of…
In this paper we unveil some features of a discrete-time quantum walk on the line whose coin depends on the temporal variable. After considering the most general form of the unitary coin operator, we focus on the role played by the two…
We study the asymptotic properties of nearest-neighbor random walks in 1d random environment under the influence of an external field of intensity $\lambda\in\mathbb{R}$. For ergodic shift-invariant environments, we show that the limiting…
We investigate the mixing properties of a model of reversible Markov chains in random environment, which notably contains the simple random walk on the superposition of a deterministic graph and a second graph whose vertex set has been…