Related papers: Random interlacements and the Gaussian free field
We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a…
Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…
We study random walks in random environments generated by the two-dimensional Gaussian free field. More specifically, we consider a rescaled lattice with a small mesh size and view it as a random network where each edge is equipped with an…
We propose a generative model for the spatio-temporal distribution of high dimensional categorical observations. These are commonly produced by robots equipped with an imaging sensor such as a camera, paired with an image classifier,…
We consider a random sequential adsorption process on the one-dimensional lattice with nearest-neighbor exclusion. In this model, each site $s \in \mathbb{Z}$ starts empty and we will try to occupy it in time $t_s$, where…
Via gauge-gravity duality, relaxation of far-from-equilibrium initial states in a strongly coupled gauge theory has been investigated. In the system we consider in this paper there are two ways where the state under study can deviate from…
Functional limit theorems are presented for the rescaled occupation time fluctuations process of a critical finite variance branching particle system in $R^d$ with symmetric a-stable motion starting off from either a standard Poisson random…
Recently we constructed a renormalizable field theory up to two loops for the quasi-static depinning of elastic manifolds in a disordered environment. Here we explore further properties of the theory. We show how higher correlation…
Consider a random geometric graph over a random point process in $\mathbb{R}^d$. Two points are connected by an edge if and only if their distance is bounded by a prescribed distance parameter. We show that projecting the graph onto a two…
The effect of metallic nano-particles (MNPs) on the electrostatic potential of a disordered 2D dielectric media is considered. The disorder in the media is assumed to be white-noise Coulomb impurities with normal distribution. To realize…
We analyze the behavior of an ensemble of inertial particles in a one-dimensional smooth Gaussian velocity field, in the limit of large inertia, but considering a finite correlation time for the random field. We derive in this limit a…
The sensitivity of the random field Ising model to small random perturbations of the quenched disorder is studied via exact ground states obtained with a maximum-flow algorithm. In one and two space dimensions we find a mild form of chaos,…
Random fields are commonly used for modeling of spatially (or timely) dependent stochastic processes. In this study, we provide a characterization of the intrinsic complexity of a random field in terms of its second order statistics, e.g.,…
To investigate order-order interfaces, we perform multimagnetical Monte Carlo simulations of the $2D$ and $3D$ Ising model. Following Binder we extract the interfacial free energy from the infinite volume limit of the magnetic probability…
We study the critical branching random walk on $\mathbb{Z}^d$ started from a distant point $x$ and conditioned to hit some compact set $K$ in $\mathbb{Z}^d$. We are interested in the occupation time in $K$ and present its asymptotic…
We study percolation of two-sided level sets for the discrete Gaussian free field (DGFF) in 2D. For a DGFF $\varphi$ defined in a box $B_N$ with side length $N$, for $C$ large enough, there exist low crossings in the set of vertices $z$…
We study the trajectory of a simple random walk on a d-regular graph with d>2 and locally tree-like structure as the number n of vertices grows. Examples of such graphs include random d-regular graphs and large girth expanders. For these…
In the paper the rescaled occupation time fluctuation process of a certain empirical system is investigated. The system consists of particles evolving independently according to \alpha-stable motion in R^d, \alpha<d<2\alpha. The particles…
Random matrices whose entries come from a stationary Gaussian process are studied. The limiting behavior of the eigenvalues as the size of the matrix goes to infinity is the main subject of interest in this work. It is shown that the…
This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of…