Related papers: Continuum percolation for Gibbsian point processes…
We consider two-dimensional dependent dynamical site percolation where sites perform majority dynamics. We introduce the critical percolation function at time t as the infimum density with which one needs to begin in order to obtain an…
In a previous paper, the authors introduced an approach to prove that the statistics of the extremes of a log-correlated Gaussian field converge to a Poisson-Dirichlet variable at the level of the Gibbs measure at low temperature and under…
The continuum random cluster model is defined as a Gibbs modification of the stationary Boolean model in $\mathbb{R}^d$ with intensity $z>0$ and the law of radii $Q$. The formal unormalized density is given by $q^{N_{cc}}$ where $q>0$ is a…
We consider a collection of fully coupled weakly interacting diffusion processes moving in a two-scale environment. We study the moderate deviations principle of the empirical distribution of the particles' positions in the combined limit…
We propose a method based on cluster expansion to study the low activity/high temperature phase of a continuous particle system confined in a finite volume, interacting through a stable and finite range pair potential with negative minimum…
The percolation transitions on hyperbolic lattices are investigated numerically using finite-size scaling methods. The existence of two distinct percolation thresholds is verified. At the lower threshold, an unbounded cluster appears and…
We study the dynamical percolation transition of the geometrical clusters in the two-dimensional Ising model when it is subjected to a pulsed field below the critical temperature. The critical exponents are independent of the temperature…
We argue that clustering of color sources, leading to the percolation transition, may be the way to achieve deconfinement in heavy ion collisions. The critical density for percolation is related to the effective critical temperature of the…
Using grand canonical Monte Carlo simulations, we investigate the percolation behavior of a square well fluid with an ultra-short range of attraction in three dimension (3D) and in confined geometry. The latter is defined through two…
We consider the behavior of the Gaussian concentration bound (GCB) under stochastic time evolution. More precisely, we consider a Markovian diffusion process on $\mathbb{R}^d$ and start the process from an initial distribution $\mu$ that…
We study the percolation of FINITE-SIZED objects on two- and three-dimensional lattices. Our motivation stems, on one hand from some recent interesting experimental results on transport properties of impurity-doped oxide perovskites and on…
We propose a method of studying the continuous percolation of aligned objects as a limit of a corresponding discrete model. We show that the convergence of a discrete model to its continuous limit is controlled by a power-law dependency…
In this paper, we want to clarify the Gibbs phenomenon when continuous and discontinuous finite elements are used to approximate discontinuous or nearly discontinuous PDE solutions from the approximation point of view. For a simple step…
Gibbs states are a natural model of quantum matter at thermal equilibrium. We investigate the role of external fields in shaping the entanglement structure and computational complexity of high-temperature Gibbs states. External fields can…
We show numeric evidence that, at low enough temperatures, the potential energy density of a glass-forming liquid fluctuates over length scales much larger than the interaction range. We focus on the behavior of translationally invariant…
We introduce a method to estimate continuum percolation thresholds and illustrate its usefulness by investigating geometric percolation of non-interacting line segments and disks in two spatial dimensions. These examples serve as models for…
We analyze the Block Averaging Transformation applied to the two--dimensional Ising model in the uniqueness region. We discuss the Gibbs property of the renormalized measure and the convergence of renormalized potential under iteration of…
We examine the minimization of information entropy for measures on the phase space of bounded domains, subject to constraints that are averages of grand canonical distributions. We describe the set of all such constraints and show that it…
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…
We investigate properties of two-dimensional finite-scale percolation systems whose size along the current flow is smaller than the perpendicular size. Successive thresholds of appearing multiple percolation channels in such systems have…