Related papers: Quenched local central limit theorem for random wa…

Let \alpha ([0,1]^p) denote the intersection local time of p independent d-dimensional Brownian motions running up to the time 1. Under the conditions p(d-2)<d and d\ge 2, we prove lim_{t\to\infty}t^{-1}\log P\bigl{\alpha([0,1]^p)\ge…

In this paper, we study second order fluctuations for the size of the range of a critical branching random walk (BRW) in $\mathbb Z^d$. We consider the BRW with geometric offspring indexed by the Kesten tree, and show that the size of its…

We consider continuous-time random walk models described by arbitrary sojourn time probability density functions. We find a general expression for the distribution of time-averaged observables for such systems, generalizing some recent…

Following similar analysis to that in Lacoin (PTRF 159, 777-808, 2014), we can show that the quenched critical point for self-avoiding walk on random conductors on the d-dimensional integer lattice is almost surely a constant, which does…

We propose a discrete analogue for the boundary local time of reflected diffusions in bounded Lipschitz domains. This discrete analogue, called the discrete local time, can be effectively simulated in practice and is obtained pathwise from…

We derive sub-Gaussian bounds for the annealed transition density of the simple random walk on a high-dimensional loop-erased random walk. The walk dimension that appears in these is the exponent governing the space-time scaling of the…

We consider a random walk on a random graph $(V,E)$, where $V$ is the set of open sites under i.i.d. Bernoulli site percolation on the multi-dimensional integer set $\mathbf{Z}^d$, and the transition probabilities of the walk are generated…

We consider a branching random walk with immigration in a random environment, where the environment is a stationary and ergodic sequence indexed by time. We focus on the asymptotic properties of the sequence of measures $(Z_n)$ that count…

We prove a central limit theorem for random walks with finite variance on linear groups.

The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which…

We prove a {\it{quenched}} large deviation principle (LDP) for a simple random walk on a supercritical percolation cluster on $\Z^d$, $d\geq 2$.. We take the point of view of the moving particle and first prove a quenched LDP for the…

We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to the study of dependent random variables sampled by a $\bbZ$-valued transient random walk. This extends the results…

We consider a random walk in a random environment (RWRE) on the strip of finite width $\mathbb{Z} \times \{1,2,\ldots,d\}$. We prove both quenched and averaged large deviation principles for the position and the hitting times of the RWRE.…

We consider homogeneous open quantum random walks on a lattice with finite dimensional local Hilbert space and we study in particular the position process of the quantum trajectories of the walk. We prove that the properly rescaled position…

We prove quenched invariance principle for simple random walk on the unique infinite percolation cluster for a general class of percolation models on Z^d, d>=2, with long-range correlations introduced in arXiv:1212.2885, solving one of the…

We investigate the use of discrete-time quantum walks to sample from an almost-uniform distribution, in the absence of any external source of randomness. Integers are encoded on the vertices of a cycle graph, and a quantum walker evolves…

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 Ergodic Properties of Random Walks in stationary ergodic environments without uniform ellipticity under a minimal assumption. There are two main components in our work. The first step is to adopt the arguments of Lawler to…

In this paper, we study a class of unbalanced step-reinforced random walks that unifies the elephant random walk, the positively step-reinforced random walk, and the negatively step-reinforced random walk. By establishing a connection with…

We establish the (non-lattice) local limit theorem for products of i.i.d. random variables on an arbitrary simply connected nilpotent Lie group $G$, where the variables are allowed to be non-centered. Our result also improves on the known…