Related papers: Scaling limits for random fields with long-range d…

The main goal of this article is to understand how the length spectrum of a random surface depends on its genus. Here a random surface means a surface obtained by randomly gluing together an even number of triangles carrying a fixed metric.…

This work is concerned with fractional Gaussian fields, i.e. Gaussian fields whose covariance operator is given by the inverse fractional Laplacian $(-\Delta)^{-s}$ (where, in particular, we include the case $s >1$). We define a lattice…

We consider the Gaussian interface model in the presence of random external fields, that is the finite volume (random) Gibbs measure on $\mathbb{R}^{\Lambda_N}$, $\Lambda_N=[-N, N]^d\cap \mathbb{Z}^d$ with Hamiltonian $H_N(\phi)=…

We obtain a complete description of local anisotropic scaling limits for a class of fractional random fields $X$ on ${\mathbb{R}}^2$ written as stochastic integral with respect to infinitely divisible random measure. The scaling procedure…

We study numerically the zero temperature Random Field Ising Model on cubic lattices of various linear sizes $ 6 \le L \le 90 $ in three dimensions with the purpose of verifying the validity of universality for disordered systems. For each…

Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…

We study the scaling limit of a divisible sandpile model associated to a truncated $\alpha$-stable random walk. We prove that the limiting distribution is related to an obstacle problem for a truncated fractional Laplacian. We also provide,…

Let $r=r(n)$ be a sequence of integers such that $r\leq n$ and let $X_1,\ldots,X_{r+1}$ be independent random points distributed according to the Gaussian, the Beta or the spherical distribution on $\mathbb{R}^n$. Limit theorems for the…

We study the competition between random multiplicative growth and redistribution/migration in the mean-field limit, when the number of sites is very large but finite. We find that for static random growth rates, migration should be strong…

We study the length of cycles in the model of spatial random permutations in Euclidean space. In this model, for given length $L$, density $\rho$, dimension $d$ and jump density $\varphi$, one samples $\rho L^d$ particles in a…

We study a random partial covering model on the $(d-1)$-dimensional unit sphere, where $N$ spherical caps are placed independently and uniformly at random, each covering a surface fraction of $1/N$. This model provides a continuous…

Let $u(t,\mathbf{x}),\ t>0,\ \mathbf{x}\in \mathbb{R}^{n},$ be the spatial-temporal random field arising from the solution of a relativistic diffusion equation with the spatial-fractional parameter $\alpha\in (0,2)$ and the mass parameter…

Spatial random permutations were originally studied due to their connections to Bose-Einstein condensation, but they possess many interesting properties of their own. For random permutations of a regular lattice with periodic boundary…

The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…

In large dimension, we study the asymptotic behavior of the mean number of critical points with index k below a level u for an isotropic centered Gaussian random field defined on a family of subsets of $R^d$ depending on d. We prove the…

The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to…

A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…

A discrete gradient model for interfaces is studied. The interaction potential is a non-convex perturbation of the quadratic gradient potential. Based on a representation for the finite volume Gibbs measure obtained via a renormalization…

We consider discrete Gaussian free fields with ergodic random conductances on a class of random subgraphs of $\mathbb{Z}^{d}$, $d \geq 2$, including i.i.d.\ supercritical percolation clusters, where the conductances are possibly unbounded…

We consider the discrete Gaussian Free Field (DGFF) in scaled-up (square-lattice) versions of suitably regular continuum domains $D\subset\mathbb C$ and describe the scaling limit, including local structure, of the level sets at heights…