相关论文: Generalised Wigner surmise for 2x2 random matrices
We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…
We equip the polytope of $n\times n$ Markov matrices with the normalized trace of the Lebesgue measure of $\mathbb{R}^{n^2}$. This probability space provides random Markov matrices, with i.i.d. rows following the Dirichlet distribution of…
We obtain generalized Wintgen inequalities for submanifolds in conformally flat manifolds. We give some applications for submanifolds in a Riemannian manifold of quasi-constant curvature. Equality cases are also considered.
We consider 1d random Hermitian $N\times N$ block band matrices consisting of $W\times W$ random Gaussian blocks (parametrized by $j,k \in\Lambda=[1,n]\cap \mathbb{Z}$, $N=nW$) with a fixed entry's variance…
Following E. Wigner's original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix $H$ yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability.…
The Nearest Neighbour Spacing (NNS) distribution can be computed for generalized symmetric 2x2 matrices having different variances in the diagonal and in the off-diagonal elements. Tuning the relative value of the variances we show that the…
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…
Mutual space-frequency distribution is proposed and it is shown that Wigner and Weyl distribution functions are only particular cases of these distribution. Mutual distribution for Gaussian signal is analytically obtained. The simple…
We prove generalised row and column removal results for decomposition numbers of spin representations of symmetric groups in characteristic 2, similar to Donkin's results for decomposition numbers of representations of symmetric groups.
We study the universal properties of distributions of eigenvalues of random matrices in the large $N$ limit. The distributions fall in universality classes characterized entirely by the support of the spectral density.
We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the…
We consider large non-Hermitian real or complex random matrices $X$ with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of…
A family of generalized binomial probability distributions attached to Landau levels on the Riemann sphere is introduced by constructing a kind of generalized coherent states. Their main statistical parameters are obtained explicitly. As…
We study statistical properties of a class of band random matrices which naturally appears in systems of interacting particles. The local spectral density is shown to follow the Breit-Wigner distribution in both localized and delocalized…
We prove that the linear statistics of the eigenvalues of a Wigner matrix converge to a universal Gaussian process on all mesoscopic spectral scales, i.e. scales larger than the typical eigenvalue spacing and smaller than the global extent…
Williamson's theorem states that if $A$ is a $2n \times 2n$ real symmetric positive definite matrix then there exists a $2n \times 2n$ real symplectic matrix $M$ such that $M^T A M=D \oplus D$, where $D$ is an $n \times n$ diagonal matrix…
This work sets the matrix variate Birnbaum-Saunders theory in the context of singular distributions and elliptical models. The so termed singular matrix variate generalised Birnbaum-Saunders distribution is obtained with respect the…
We present some properties of measures (q-Gaussian) that orthogonalize the set of q-Hermite polynomials. We also present an algorithm for simulating i.i.d. sequences of random variables having q-Gaussian distribution.
The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a…
Two approaches are suggested to the definition of asymmetric generalized Weibull distribution. These approaches are based on the representation of the two-sided Weibull distributions as variance-mean normal mixtures or more general…