Related papers: Random walks in space time mixing environments
The mixing time of a discrete-time quantum walk on the hypercube is considered. The mean probability distribution of a Markov chain on a hypercube is known to mix to a uniform distribution in time O(n log n). We show that the mean…
The random walk in Dirichlet environment is a random walk in random environment where the transition probabilities are independent Dirichlet random variables. This random walk exhibits a property of statistical invariance by time-reversal…
We introduce a variation of the step-reinforced random walk with general memory. For the diffusive regime, we establish a functional invariance principle and show that, given suitable conditions on the memory sequence, the arising limiting…
The mixing process of discrete-time quantum walks on one-dimensional lattices is revisited in a setting where the walker is coupled to an environment, and the time evolution of the walker and the environment is unitary. The mixing process…
We study the random walk in random environment on {0,1,2,...}, where the environment is subject to a vanishing (random) perturbation. The two particular cases we consider are: (i) random walk in random environment perturbed from Sinai's…
We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…
We consider a one dimensional random walk in random environment that is uniformly biased to one direction. In addition to the transition probability, the jump rate of the random walk is assumed to be spatially inhomogeneous and random. We…
Random walks on expanders play a crucial role in Markov Chain Monte Carlo algorithms, derandomization, graph theory, and distributed computing. A desirable property is that they are rapidly mixing, which is equivalent to having a spectral…
We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogenous random walks in the plane which interlace two…
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…
We prove a law of large numbers for a class of multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions, which hold when the environment is a weak mixing field in the sense of…
Consider a one-dimensional shift-invariant attractive spin-flip system in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied sites has a local drift to the right but on…
This paper states a law of large numbers for a random walk in a random iid environment on ${\mathbb Z}^d$, where the environment follows some Dirichlet distribution. Moreover, we give explicit bounds for the asymptotic velocity of the…
We consider the maximum $M_t$ of branching random walk in a space-inhomogeneous random environment on $\mathbb{Z}$. In this model the branching rate while at some location $x\in\mathbb{Z}$ is randomized in an i.i.d. manner. We prove that…
We study the asymptotic behaviour of a version of the one-dimensional Mott random walk in a regime that exhibits severe blocking. We establish that, for any fixed time, the appropriately-rescaled Mott random walk is situated between two…
Restrictions to molecular motion by barriers (membranes) are ubiquitous in biological tissues, porous media and composite materials. A major challenge is to characterize the microstructure of a material or an organism nondestructively using…
We show that random walk in uniformly elliptic i.i.d. environment in dimension $\geq5$ has at most one non zero limiting velocity. In particular this proves a law of large numbers in the distributionally symmetric case and establishes…
Attributing a positive value \tau_x to each x in Z^d, we investigate a nearest-neighbour random walk which is reversible for the measure with weights (\tau_x), often known as "Bouchaud's trap model". We assume that these weights are…
We study the asymptotic behaviour of random walks in i.i.d. random environments on $\Z^d$. The environments need not be elliptic, so some steps may not be available to the random walker. We prove a monotonicity result for the velocity (when…
We consider random walkers that deform the medium as they move, enabling a faster motion in regions which have been recently visited. This induces an effective attraction between walkers mediated by the medium, which can be regarded as a…