Related papers: A numerical study of the 3D random interchange and…
An anisotropic random barrier model is presented, in which the transition probabilities in different directions have different probability density functions. At low temperatures, the anisotropic long--time diffusion coefficients, obtained…
We study the crossover behaviors that can be observed in the high-temperature phase of three-dimensional dilute spin systems, using a field-theoretical approach. In particular, for randomly dilute Ising systems we consider the…
Consider n unit intervals, say [1,2], [3,4], ..., [2n-1,2n]. Identify their endpoints in pairs at random, with all (2n-1)!! = (2n-1) (2n-3) ... 3 1 pairings being equally likely. The result is a collection of cycles of various lengths, and…
The first passage statistics of a continuous time random walker with Poisson distributed jumps on one and two dimensional infinite lattices is investigated. An exact expression for the probability of first return to the origin in one…
Random walks with a fixed bias direction on randomly diluted cubic lattices far above the percolation threshold exhibit log-periodic oscillations in the effective exponent versus time. A scaling argument accounts for the numerical results…
We study the length of short cycles on uniformly random metric maps (also known as ribbon graphs) of large genus using a Teichm\"uller theory approach. We establish that, as the genus tends to infinity, the length spectrum converges to a…
We explore exchange coupling of a pair of spins in a double dot and in an optical lattice. Our algorithm uses the frequency of exchanges in a bosonic path integral, evaluated with Monte Carlo. This algorithm is simple enough to be a "black…
For $d\ge 3$ we construct a new coupling of the trace left by a random walk on a large $d$-dimensional discrete torus with the random interlacements on $\mathbb Z^d$. This coupling has the advantage of working up to macroscopic subsets of…
The phase diagram of the O(n) model, in particular the special case $n=0$, is studied by means of transfer-matrix calculations on the loop representation of the O(n) model. The model is defined on the square lattice; the loops are allowed…
We study the distribution of cycle lengths in models of nonuniform random permutations with cycle weights. We identify several regimes. Depending on the weights, the length of typical cycles grows like the total number $n$ of elements, or a…
On the space of $\pm 1$ spin configurations on the 3$d$-square lattice, we consider the \emph{shaken dynamics}, a parallel Markovian dynamics that can be interpreted in terms of Probabilistic Cellular Automata. The transition probabilities…
At low temperature in the epsilon regime of QCD the low-end of the Dirac spectrum is described by random matrix theory. In contrast, there has been no similarly well established staistical description in the high temperature, chirally…
The measurements of the magnetic and nematic correlation lengths in a generalization of the two dimensional XY model on the square lattice are presented using classical Monte Carlo simulation. The full phase diagram is re-examined based on…
It is reported that the characteristic relations of type-II and type-III intermittencies, with respective local Poincar$\acute{e}$ maps of $x_{n+1}= (1+\epsilon)x_n + a x^3_n$ and $x_{n+1}= - (1+\epsilon)x_n - a x^3_n$, are both $- ln…
We consider continuous time random interlacements on $\mathbb{Z}^d$, $d \ge 3$, and characterize the distribution of the corresponding stationary random field of occupation times. When d = 3, we relate this random field to the…
This paper treats a random collision model of three species, which is represented by the random time change of three standard Poisson processes. The prey-predator relation in the random collision model looks like paper-scissors-stone game,…
We consider a thin droplet that spreads over a flat, horizontal and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes…
Estimation of crossed random effects models commonly requires computational costs that grow faster than linearly in the sample size $N$, often as fast as $\Omega(N^{3/2})$, making them unsuitable for large data sets. For non-Gaussian…
In this paper we consider a telegraph equation with time-dependent coefficients, governing the persistent random walk of a particle moving on the line with a time-varying velocity $c(t)$ and changing direction at instants distributed…
In spatial networks vertices are arranged in some space and edges may cross. When arranging vertices in a 1-dimensional lattice edges may cross when drawn above the vertex sequence as it happens in linguistic and biological networks. Here…