相关论文: Gaussian fluctuations for \beta Ensembles

The performance of spectral clustering relies on the fluctuations of the entries of the eigenvectors of a similarity matrix, which has been left uncharacterized until now. In this letter, it is shown that the signal $+$ noise structure of a…

The aim of this paper is to identify the limit in a high temperature regime of classical beta ensembles on the real line and related eigenvalue processes by using the Markov--Krein transform. We show that the limiting measure of Gaussian…

We study asymptotics of reducible representations of the symmetric groups S_q for large q. We decompose such a representation as a sum of irreducible components (or, alternatively, Young diagrams) and we ask what is the character of a…

We review our previous work on the the calculation of the stress-energy tensor for a scalar particle in the background metric of different types of spherical impulsive, spherical shock and plane impulsive gravitational waves.

We study the fluctuations of the largest eigenvalue $\lambda_{\max}$ of $N \times N$ random matrices in the limit of large $N$. The main focus is on Gaussian $\beta$-ensembles, including in particular the Gaussian orthogonal ($\beta=1$),…

We numerically analyse the behavior of the full distribution of collective observables in quantum spin chains. While most of previous studies of quantum critical phenomena are limited to the first moments, here we demonstrate how quantum…

We consider the probability of two large gaps (intervals without eigenvalues) in the bulk scaling limit of the Gaussian Unitary Ensemble of random matrices. We determine the multiplicative constant in the asymptotics. We also provide the…

Spectral statistics and correlations are the usual way to study the presence or absence of quantum chaos in quantum systems. We present our investigation on the study of the fluctuation average and variance of certain correlation functions…

We study low--temperature non Gaussian thermal fluctuations of a system of classical particles around a (hypothetical) crystalline ground state. These thermal fluctuations are described by the behaviour of a system of long range interacting…

We find the precise rate at which the empirical measure associated to a $\beta$-ensemble converges to its limiting measure. In our setting the $\beta$-ensemble is a random point process on a compact complex manifolds distributed according…

We consider fluctuations in the distribution of critical points - saddle points, minima and maxima - of random gaussian fields. We calculate the asymptotic limits of the two point correlation function for various critical point densities,…

We consider the scaling limit of linear statistics for eigenphases of a matrix taken from one of the classical compact groups. We compute their moments and find that the first few moments are Gaussian, whereas the limiting distribution is…

The aim of this note is to prove that fluctuations of uniformly random alternating sign matrices (equivalently, configurations of the six-vertex model with domain wall boundary conditions) near the boundary are described by the Gaussian…

In spite of the macroscopic character of the fluctuation amplitudes, we show that the standard inflationary distribution of primordial density fluctuations still exhibits inherently quantum mechanical correlations (which cannot be mimicked…

An error estimate for the Gauss-Lobatto quadrature formula for integration over the interval $[-1, 1]$, relative to the Jacobi weight function $w^{\alpha,\beta}(t)=(1-t)^\alpha(1+t)^\beta$, $\alpha,\beta>-1$, is obtained. This estimate…

We study analytically giant fluctuations and temporal intermittency in a stochastic one-dimensional model with diffusion and aggregation of masses in the bulk, along with influx of single particles and outflux of aggregates at the…

We study the equilibrium fluctuations for a gradient exclusion process with conductances in random environments, which can be viewed as a central limit theorem for the empirical distribution of particles when the system starts from an…

We study the problem of continuum percolation in infinite volume Gibbs measures for particles with an attractive pair potential, with a focus on low temperatures (large $\beta$). The main results are bounds on percolation thresholds…

For arbitrary $\beta > 0$, we use the orthogonal polynomials techniques developed by R. Killip and I. Nenciu to study certain linear statistics associated with the circular and Jacobi $\beta$ ensembles. We identify the distribution of these…

This paper discusses two distinct, but related issues in quantum fluctuation effects. The first is the frequency spectrum which can be assigned to one loop quantum processes. The formal spectrum is a flat one, but the finite quantum effects…