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We consider the Rosenzweig-Porter model of random matrix which interpolates between Poisson and gaussian unitary statistics and compute exactly the two-point correlation function. Asymptotic formulas for this function are given near 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…

We study asymptotic expansions of spin-spin correlation functions for the XXZ Heisenberg chain in the critical regime. We use the fact that the long-distance effects can be described by the Gaussian conformal field theory. Comparing exact…

Random fields play a central role in the analysis of spatially correlated data and, as a result, have a significant impact on a broad array of scientific applications. This paper studies the cepstral random field model, providing recursive…

We develop a path-integral formalism to study the formation of large-scale structures in the universe. Starting from the equations of motion of hydrodynamics (single-stream approximation) we derive the action which describes the statistical…

The effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact…

We establish a rigorous asymptotic theory for the joint estimation of roughness and scale parameters in two-dimensional Gaussian random fields with power-law generalized covariances \cite{Matheron1973, Stein1999, Yaglom1987}. Our main…

In this work we propose a new numerical method to evaluate the critical point, the susceptibility critical exponent and the correlation length critical exponent of the three dimensional Ising model without external field using an algorithm…

This paper is concerned with the existence of multiple points of Gaussian random fields. Under the framework of Dalang et al. (2017), we prove that, for a wide class of Gaussian random fields, multiple points do not exist in critical…

We consider the d-dimensional massless free field localized by a delta-pinning of strength e. We study the asymptotics of the variance of the field, and of the decay-rate of its 2-point function, as e goes to zero, for general Gaussian…

We consider a symmetric exclusion process on a discrete interval of $S$ points with various boundary conditions at the endpoints. We study the asymptotic decay of correlations as $S\to\infty$. The main result is asymptotic independence of a…

This is the second in a series of two works which study the discrete Gaussian free field on the binary tree when all leaves are conditioned to be positive. In the first work ("Gaussian free field on the tree subject to a hard wall I:…

Motivated by the papers of Piterbarg (2004) and H\"{u}sler (2004), in this paper the asymptotic relation between the maximum of a continuous dependent homogeneous Gaussian random field and the maximum of this field sampled at discrete time…

We establish a general criterion for the positivity of the variance of a chaotic component of local functionals of stationary vector-valued Gaussian fields. This criterion is formulated in terms of the spectral properties of the covariance…

This paper is concerned with the asymptotic analysis of sojourn times of random fields with continuous sample paths. Under a very general framework we show that there is an interesting relationship between tail asymptotics of sojourn times…

We study the correlation between the total number of critical points of random spherical harmonics and the number of critical points with value in any interval $I \subset \mathbb{R}$. We show that the correlation is asymptotically zero,…

We study the asymptotics of correlations and nearest neighbor spacings between zeros and holomorphic critical points of $p_N$, a degree N Hermitian Gaussian random polynomial in the sense of Shiffman and Zeldtich, as N goes to infinity. By…

Critical points of a scalar quantitiy are either extremal points or saddle points. The character of the critical points is determined by the sign distribution of the eigenvalues of the Hessian matrix. For a two-dimensional homogeneous and…

A sequence of $n$-particle approximations for the system of Schwinger-Dyson equations is investigated in the model of a complex scalar field $\phi$ and a real scalar field $\chi$ with the interaction $g\phi^*\phi\chi$. In the first…

Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…