Related papers: Subdiffusivity of random walk on the 2D invasion p…

We study first-passage percolation on $\mathbb Z ^2$ with independent and identically distributed weights, whose common distribution is uniform on $\{a,b\}$ with $0<a<b<\infty $. Following Ahlberg and De la Riva, we consider the passage…

In this article we obtain uniform estimates on the absorption of Brownian motion by porous interfaces surrounding a compact set. An important ingredient is the construction of certain resonance sets, which are hard to avoid for Brownian…

We consider a simple random walk on a discrete torus (Z/NZ)^d with dimension d at least 3 and large side length N. For a fixed constant u > 0, we study the percolative properties of the vacant set, consisting of the set of vertices not…

We consider a one-dimensional simple random walk surviving among a field of static soft traps : each time it meets a trap the walk is killed with probability 1--e --$\beta$ , where $\beta$ is a positive and fixed parameter. The positions of…

Directed covers of finite graphs are also known as periodic trees or trees with finitely many cone types. We expand the existing theory of directed covers of finite graphs to those of infinite graphs. While the lower growth rate still…

We derive an estimate for the distance, measured in lattice spacings, inside two-dimensional critical percolation clusters from the origin to the boundary of the box of side length $2n$, conditioned on the existence of an open connection.…

We study asymptotic properties of spatially non-homogeneous random walks with non-integrable increments, including transience, almost-sure bounds, and existence and non-existence of moments for first-passage and last-exit times. In our…

We consider first-passage percolation on the edges of $\mathbb{Z}^2 \times \{1, \cdots, k\},$ namely the slab $\mathbb{S}_k$ of width $k$. Each edge is assigned independently a passage time of either 0 (with probability $p_c(\mathbb{S}_k)$)…

Let $ p_n(x)=\int_0^\infty J_0(xt)[J_0(t)]^n xt\,\mathrm{d}\, t$ be Kluyver's probability density for $n$-step uniform random walks in the Euclidean plane. Through connection to a similar problem in 2-dimensional quantum field theory, we…

In this work we extend the quenched local limit theorem obtained by the authors in [BBDS23]. More precisely, we consider a directed random walk on the backbone of the supercritical oriented percolation cluster in dimensions $d+1$ with…

We prove the existence of scaling limits for the projection on the backbone of the random walks on the Incipient Infinite Cluster and the Invasion Percolation Cluster on a regular tree. We treat these projected random walks as randomly…

Consider critical site percolation on $\mathbb{Z}^d$ with $d \geq 2$. We prove a lower bound of order $n^{- d^2}$ for point-to-point connection probabilities, where $n$ is the distance between the points. Most of the work in our proof…

We study cover times of subsets of ${\mathbb Z}^2$ by a two-dimensional massive random walk loop soup. We consider a sequence of subsets $A_n \subset {\mathbb Z}^2$ such that $|A_n| \to \infty$ and determine the distributional limit of…

We continue our study of the inventory accumulation introduced by Sheffield (2011), which encodes a random planar map decorated by a collection of loops sampled from the critical Fortuin-Kasteleyn (FK) model. We prove various \emph{local…

We consider general classes of lattice clusters, including various kinds of animals and trees on different lattices. We prove that if a given local configuration ("pattern") of sites and bonds can occur in large clusters, then it occurs at…

We consider in this paper subdiffusion in a system with a thin membrane. The subdiffusion parameters are the same in both parts of the system separated by the membrane. Using the random walk model with discrete time and space variables the…

We study a version of compact directed percolation (CDP) in one dimension in which occupation of a site for the first time requires that a "mine" or antiparticle be eliminated. This process is analogous to the variant of directed…

Coalescing-branching random walks, or {\em cobra walks} for short, are a natural variant of random walks on graphs that can model the spread of disease through contacts or the spread of information in networks. In a $k$-cobra walk, at each…

We construct an exact expression for the site percolation threshold p_c on a quasi-regular tree, and a related exact lower bound for a quasi-regular graph. Both are given by the inverse spectral radius of the appropriate Hashimoto matrix…

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…