Related papers: An elementary approach to Gaussian multiplicative …
The aim of the present letter is to explain the `critical behaviour' observed in numerical studies of spherically symmetric gravitational collaps of a perfect fluid. A simple expression results for the critical index $\gamma$ of the black…
Let $\a$ be a complex random variable with mean zero and bounded variance $\sigma^{2}$. Let $N_{n}$ be a random matrix of order $n$ with entries being i.i.d. copies of $\a$. Let $\lambda_{1}, ..., \lambda_{n}$ be the eigenvalues of…
We prove that for Gaussian random normal matrices the correlation function has universal behavior. Using the technique of orthogonal polynomials and identities similar to the Christoffel-Darboux formula, we find that in the limit, as the…
We demonstrate that generalized entanglement [Barnum {\em et al.}, Phys. Rev. A {\bf 68}, 032308 (2003)] provides a natural and reliable indicator of quantum chaotic behavior. Since generalized entanglement depends directly on a choice of…
Many low temperature disordered systems are expected to exhibit Poisson-Dirichlet (PD) statistics. In this paper, we focus on the case when the underlying disorder is a logarithmically correlated Gaussian process $\phi_N$ on the box…
Several proofs of the monotonicity of the non-Gaussianness (divergence with respect to a Gaussian random variable with identical second order statistics) of the sum of n independent and identically distributed (i.i.d.) random variables were…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
This is the second part of a series of papers where we consider questions related to the tail profile of the bulk/boundary quotients of Gaussian multiplicative chaos measures appearing in boundary Liouville conformal field theory. In this…
We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…
The universality phenomenon asserts that the distribution of the eigenvalues of random matrix with i.i.d. zero mean, unit variance entries does not depend on the underlying structure of the random entries. For example, a plot of the…
The random trigonometric series $\sum_{n=1}^\infty \rho_n \cos (nt +\omega_n)$ on the circle $\mathbb{T}$ are studied under the conditions $\sum |\rho_n|^2=\infty$ and $\rho_n\to 0$, where $\{\omega_n\}$ are iid and uniformly distributed on…
Gaussian random processes which variances reach theirs maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximums of theirs trajectories have been evaluated using Double Sum Method…
We investigate the universality of correlation functions of chaotic and disordered quantum systems as an external parameter is varied. A new, general scaling procedure is introduced which makes the theory invariant under reparametrizations.…
We prove that the $k$-th positive integer moment of partial sums of Steinhaus random multiplicative functions over the interval $(x, x+H]$ matches the corresponding Gaussian moment, as long as $H\ll x/(\log x)^{2k^2+2+o(1)}$ and $H$ tends…
We establish the universality of the singular numbers in random matrix products over $\mathrm{GL}_n(\mathbb{Q}_p)$ as the number of products approaches infinity, with a fixed $n\ge 1$. We demonstrate that, under a broad class of…
We consider the problem of disorder chaos in the spherical mean-field model. It is concerned about the behavior of the overlap between two independently sampled spin configurations from two Gibbs measures with the same external parameters.…
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…
We study the effects of an arbitrary external perturbation in the statistical properties of the S-matrix of quantum chaotic scattering systems in the limit of isolated resonances. We derive, using supersymmetry, an exact non-perturbative…
In this paper we discuss general tridiagonal matrix models which are natural extensions of the ones given by Dumitriu and Edelman. We prove here the convergence of the distribution of the eigenvalues and compute the limiting distributions…
We obtain new bounds for the optimal matching cost for empirical measures with unbounded support. For a large class of radially symmetric and rapidly decaying probability laws, we prove for the first time the asymptotic rate of convergence…