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In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of…
We prove that the Fourier transform of the properly-scaled normalized two-point function for sufficiently spread-out long-range oriented percolation with index \alpha>0 converges to e^{-C|k|^{\alpha\wedge2}} for some C\in(0,\infty) above…
We consider long-range Bernoulli bond percolation on the $d$-dimensional hierarchical lattice in which each pair of points $x$ and $y$ are connected by an edge with probability $1-\exp(-\beta\|x-y\|^{-d-\alpha})$, where $0<\alpha<d$ is…
Bourgade, Nikeghbali and Rouault recently proposed a matrix model for the circular Jacobi $\beta$-ensemble, which is a generalization of the Dyson circular $\beta$-ensemble but equipped with an additional parameter $b$, and further studied…
We study the joint asymptotic behavior of spacings between particles at the edge of multilevel Dyson Brownian motions, when the number of levels tends to infinity. Despite the global interactions between particles in multilevel Dyson…
We use Monte Carlo simulations to measure the spin-spin correlation function in the disordered phase of two-dimensional $q$-state Potts models with $q=10,15$, and $20$ at the first-order transition point $\beta_t$. To extract the…
We study the real, bounded-variables process (X_n) defined by a k-term recurrence relation X_{n+k} ={\phi}(X_n, ... , X_{n+k-1}). We prove the decay of correlations, mainly under purely analytic hypotheses concerning the function {\phi} and…
This is the first of two papers on the critical behaviour of bond percolation models in high dimensions. In this paper, we obtain strong joint control of the critical exponents eta and delta, for the nearest-neighbour model in very high…
In this article, results have been presented for the two-time correlation functions for a free and a harmonically confined Brownian particle in a simple shear flow. For a free Brownian particle, the motion along the direction of shear…
In this paper, we study the truncated two-particle correlation function in particle systems with long range interactions. For Coulombian and soft potentials, we define and give well-posedness results for the equilibrium correlations. In the…
The Airy$_\beta$ line ensemble is a random collection of continuous curves, which should serve as a universal edge scaling limit in problems related to eigenvalues of random matrices and models of 2d statistical mechanics. This line…
We study visibility inside the vacant set of three models in $\mathbb R^d$ with slow decay of spatial correlations: Brownian interlacements, Poisson cylinders and Poisson-Boolean models. Let $Q_x$ be the radius of the largest ball centered…
The goal of this paper is to provide estimates leading to a direct proof of the exponential decay of the n-point correlation functions for certain unbounded models of Kac type. The methods are based on estimating higher order derivatives of…
We consider n one-dimensional Brownian motions, such that n/2 Brownian motions start at time t=0 in the starting point a and end at time t=1 in the endpoint b and the other n/2 Brownian motions start at time t=0 at the point -a and end at…
We consider near-critical two-dimensional statistical systems with boundary conditions inducing phase separation on the strip. By exploiting low-energy properties of two-dimensional field theories, we compute arbitrary $n$-point correlation…
We analytically describe the decay to equilibrium of generic observables of a non-integrable system after a perturbation in the form of a random matrix. We further obtain an analytic form for the time-averaged fluctuations of an observable…
Dunkl processes are generalizations of Brownian motion obtained by using the differential-difference operators known as Dunkl operators as a replacement of spatial partial derivatives in the heat equation. Special cases of these processes…
In this article we study the Dyson Bessel process, which describes the evolution of singular values of rectangular matrix Brownian motions, and prove a large deviation principle for its empirical particle density. We then use it to obtain…
We establish a Brownian extension to Selberg's central limit theorem for the Riemann zeta function. This implies various limiting distributions for $\zeta$, including an analogue of the reflection principle for the maximum of the Brownian…
We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or…