Related papers: General truncated linear statistics for the top ei…
Let $M_n$ be a $n \times n$ Wigner or sample covariance random matrix, and let $\mu_1(M_n), \mu_2(M_n), ..., \mu_n(M_n)$ denote the unordered eigenvalues of $M_n$. We study the fluctuations of the partial linear eigenvalue statistics $$…
We develop a method that relates the truncated cumulant-function of the fourth order with the L\'evian cumulant-function. This gives us explicit formulas for the L\'evy-parameters, which allow a real-time analysis of the state of a…
Statistical properties of infinite products of random isotropically distributed matrices are investigated. Both for continuous processes with finite correlation time and discrete sequences of independent matrices, a formalism that allows to…
We study the limiting behavior of smooth linear statistics of the spectrum of random permutation matrices in the mesoscopic regime, when the permutation follows one of the Ewens measures on the symmetric group. If we apply a smooth enough…
This paper is concerned with the asymptotic empirical eigenvalue distribution of a non linear random matrix ensemble. More precisely we consider $M= \frac{1}{m} YY^*$ with $Y=f(WX)$ where $W$ and $X$ are random rectangular matrices with…
Let $F=F_N$ be the distribution of a finite real population of size $N$. Let $\widehat{F}=F_N$ be the empirical distribution of a sample of size $n$ drawn from the population without replacement. We prove the following remarkable {\it…
Determinantal Point Processes (DPPs), which originate from quantum and statistical physics, are known for modelling diversity. Recent research [Ghosh and Rigollet (2020)] has demonstrated that certain matrix-valued $U$-statistics (that are…
Universality of local eigenvalue statistics is one of the most striking phenomena of Random Matrix Theory, that also accounts for a lot of the attention that the field has attracted over the past 15 years. In this paper we focus on the…
We study the linear eigenvalue statistics of large random graphs in the regimes when the mean number of edges for each vertex tends to infinity. We prove that for a rather wide class of test functions the fluctuations of linear eigenvalue…
Linear Mixed Effects (LME) models have been widely applied in clustered data analysis in many areas including marketing research, clinical trials, and biomedical studies. Inference can be conducted using maximum likelihood approach if…
We introduce the truncated Gaussian graphical model (TGGM) as a novel framework for designing statistical models for nonlinear learning. A TGGM is a Gaussian graphical model (GGM) with a subset of variables truncated to be nonnegative. The…
We consider the classical trapped Riesz gas, i.e., $N$ particles at positions $x_i$ in one dimension with a repulsive power law interacting potential $\propto 1/|x_i-x_j|^{k}$, with $k>-2$, in an external confining potential of the form…
We study the statistical mechanics of classical two-dimensional "Coulomb gases" with general potential and arbitrary \beta, the inverse of the temperature. Such ensembles also correspond to random matrix models in some particular cases. The…
We apply the random-matrix theory to the car-parking problem. For this purpose, we adopt a Coulomb gas model that associates the coordinates of the gas particles with the eigenvalues of a random matrix. The nature of interaction between the…
We consider $N\times N$ Gaussian random matrices, whose average density of eigenvalues has the Wigner semi-circle form over $[-\sqrt{2},\sqrt{2}]$. For such matrices, using a Coulomb gas technique, we compute the large $N$ behavior of the…
We study a one-dimensional model for granular gases, the so-called Inelastic Maxwell Model. We show theoretically the existence of stationary solutions of the unforced case, that are characterized by an infinite average energy per particle.…
We are interested in two random matrix ensembles related to permutations: the ensemble of permutation matrices following Ewens' distribution of a given parameter $\theta >0$, and its modification where entries equal to $1$ in the matrices…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Truncated data plays an important role in the statistical analysis of astronomical observations as well as in survival analysis. The motivating example for this paper concerns a set of measurements on quasars in which there is double…
Using the theory of free random variables (FRV) and the Coulomb gas analogy, we construct stable random matrix ensembles that are random matrix generalizations of the classical one-dimensional stable L\'{e}vy distributions. We show that the…