相关论文: Mock-Gaussian Behaviour for Linear Statistics of C…
In the standard picture of structure formation, initially random-phase fluctuations are amplified by non-linear gravitational instability to produce a final distribution of mass which is highly non-Gaussian and has highly coupled Fourier…
The winding number is the topological invariant that classifies chiral symmetric Hamiltonians with one-dimensional parametric dependence. In this work we complete our study of the winding number statistics in a random matrix model belonging…
The Gaussian unitary random matrix ensembles satisfying some additional symmetry conditions are considered. The effect of these conditions on the limiting normalized counting measures and correlation functions is studied.
The classical limit problem of quantum mechanics is revisited on the basis of a scheme that enables a quantitative study of the way the quantum-classical agreement emerges while going through the intermediate mass range between the…
The construction of a statistical model for eigenfunctions of the Ising model in transverse and longitudinal fields is discussed in detail for the chaotic case. When the number of spins is large, each wave function coefficient has the…
In order to have a better understanding of finite random matrices with non-Gaussian entries, we study the $1/N$ expansion of local eigenvalue statistics in both the bulk and at the hard edge of the spectrum of random matrices. This gives…
I give a highly selective overview of the way statistical mechanics explains the microscopic origins of the time asymmetric evolution of macroscopic systems towards equilibrium and of first order phase transitions in equilibrium. These…
We consider an $n\times n$ matrix of independent real Gaussian random variables and determine the asymptotic distribution of the smallest gaps between complex eigenvalues.
The Collective Graphical Model (CGM) models a population of independent and identically distributed individuals when only collective statistics (i.e., counts of individuals) are observed. Exact inference in CGMs is intractable, and previous…
We study the fluctuations of the eigenvalues of real valued large centrosymmetric random matrices via its linear eigenvalue statistic. This is essentially a central limit theorem (CLT) for sums of dependent random variables. The dependence…
We consider two random matrix ensembles which are relevant for describing critical spectral statistics in systems with multifractal eigenfunction statistics. One of them is the Gaussian non-invariant ensemble which eigenfunction statistics…
We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. The alternative is independent identically distributed zero-mean Gaussian random variables with…
While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings…
We consider first-passage percolation on the class of "high-dimensional" graphs that can be written as an iterated Cartesian product $G\square G \square \dots \square G$ of some base graph $G$ as the number of factors tends to infinity. We…
We consider an exploration algorithm where at each step, a random number of items become active while related items get explored. Given an initial number of items $N$ growing to infinity and building on a strong homogeneity assumption, we…
We derive simple practical procedures revealing the quantum behavior of angular momentum variables by the violation of classical upper bounds on the statistics. Data analysis is minimum and definite conclusions are obtained without…
In this paper we study the distribution of level crossings for the spectra of linear families A+lambda B, where A and B are square matrices independently chosen from some given Gaussian ensemble and lambda is a complex-valued parameter. We…
Debiasing group graphical lasso estimates enables statistical inference when multiple Gaussian graphical models share a common sparsity pattern. We analyze the estimation properties of group graphical lasso, establishing convergence rates…
The log Gaussian Cox process is a flexible class of Cox processes, whose intensity surface is stochastic, for incorporating complex spatial and time structure of point patterns. The straightforward inference based on Markov chain Monte…
We derive the joint distribution of the moments $\mathrm{Tr}\, Q^{\kappa}$ ($\kappa\geq0$) of the Wigner-Smith matrix for a chaotic cavity supporting a large number of scattering channels $n$. This distribution turns out to be…