Related papers: A numerical study of the 3D random interchange and…
We consider the group of permutations of the vertices of a lattice. A random walk is generated by unit steps that each interchange two nearest neighbor vertices of the lattice. We study the heat equation on the permutation group, using the…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
In this paper we study the iterated birth process of which we examine the first-passage time distributions and the hitting probabilities. Furthermore, linear birth processes, linear and sublinear death processes at Poisson times are…
A $d$-dimensional Ising model on a lattice torus is considered. As the size $n$ of the lattice tends to infinity, a Poisson approximation is given for the distribution of the number of copies in the lattice of any given local configuration,…
The 6-vertex model is a seminal model for many domains in Mathematics and Physics. The sets of configurations of the 6-vertex model can be described as the sets of paths in multigraphs. In this article the transition probability of the…
Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…
We investigate the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain. The encounters with each subset are characterized by the boundary local time on that subset. We extend a…
We investigate a model of random spatial permutations on two-dimensional tori, and establish that the joint distribution of large cycles is asymptotically given by the Poisson--Dirichlet distribution with parameter one. The asymmetry of the…
This paper concerns a random walk that moves on the integer lattice and has zero mean and a finite variance. We obtain first an asymptotic estimate of the transition probability of the walk absorbed at the origin, and then, using the…
We study the multifractal properties of the current distribution of the three-dimensional random resistor network at the percolation threshold. For lattices ranging in size from $8^3$ to $80^3$ we measure the second, fourth and sixth…
We propose a lattice model for Dirac fermions which allows us to break the degeneracy of the node structure. In the presence of a random gap we analyze the scaling behavior of the localization length as a function of the system width within…
Two numerical strategies based on the Wang-Landau and Lee entropic sampling schemes are implemented to investigate the first-order transition features of the 3D bimodal ($\pm h$) random-field Ising model at the strong disorder regime. We…
We consider the statistical mechanics of a class of models involving close-packed loops with fugacity $n$ on three-dimensional lattices. The models exhibit phases of two types as a coupling constant is varied: in one, all loops are finite,…
We investigate the first passage statistics of active continuous time random walks with Poissonian waiting time distribution on a one dimensional infinite lattice and a two dimensional infinite square lattice. We study the small and large…
It has been noticed that when the waiting time distribution exhibits a transition from an intermediate time power law decay to a long-time exponential decay in the continuous time random walk model, a transition from anomalous diffusion to…
Random sequential adsorption of binary mixtures of extended objects on a two-dimensional triangular lattice is studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding random walks on the…
We have studied the diffusion of a single particle on a one-dimensional lattice. It is shown that, for a self-similar distribution of hopping rates, the time dependence of the mean-square displacement follows an anomalous power law…
We introduce a random interaction matrix model (RIMM) for finite-size strongly interacting fermionic systems whose single-particle dynamics is chaotic. The model is applied to Coulomb blockade quantum dots with irregular shape to describe…
We investigate the spread of correlations carried by an excitation in a 1-dimensional lattice system with high on-site energy disorder and long-range couplings with a power-law dependence on the distance ($\propto r^{-\mu}$). The increase…
In the previous paper, we studied the random-mass Dirac fermion in one dimension by using the transfer-matrix methods. We furthermore employed the imaginary vector potential methods for calculating the localization lengths. Especially we…