相关论文: Gaussian Random Matrix Models for q-deformed Gauss…
This paper combines probabilistic and algebraic techniques for computing quantum expectations of operator exponentials (and their products) of quadratic forms of quantum variables in Gaussian states. Such quadratic-exponential functionals…
We discuss a triangulated category of graded matrix factorizations of a deformed polynomial associated to the $A_{\mu}\textrm{-}$singularity. The semi-universal deformation of the $A_{\mu}\textrm{-}$singularity is given by a certain…
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…
We study the partially asymmetric exclusion process with open boundaries. We generalise the matrix approach previously used to solve the special case of total asymmetry and derive exact expressions for the partition sum and currents valid…
The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$,…
The q-Gaussian is a probability distribution generalizing the Gaussian one. In spite of a q-normal distribution is popular, there is a problem when calculating an expectation value with a corresponding normalized distribution and not a…
These notes provide an introduction to the theory of random matrices. The central quantity studied is $\tau(a)= det(1-K)$ where $K$ is the integral operator with kernel $1/\pi} {\sin\pi(x-y)\over x-y} \chi_I(y)$. Here…
Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
This investigation pertains to the construction of a class of generalised deformed derivative operators which furnish the familiar finite difference and the q-derivatives as special cases. The procedure involves the introduction of a linear…
Many models for chaotic systems consist of joining two integrable systems with incompatible constants of motion. The quantum counterparts of such models have a propagator which factorizes into two integrable parts. Each part can be…
In this note we discuss local gauge-invariant operators in noncommutative gauge theories. Inspired by the connection of these theories with the Matrix model, we give a simple construction of a complete set of gauge-invariant operators. We…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
Gaussian mixture models (GMMs) are ubiquitous in statistical learning, particularly for unsupervised problems. While full GMMs suffer from the overparameterization of their covariance matrices in high-dimensional spaces, spherical GMMs…
The deformed $\mathcal W$ algebras of type $\textsf{A}$ have a uniform description in terms of the quantum toroidal $\mathfrak{gl}_1$ algebra $\mathcal E$. We introduce a comodule algebra $\mathcal K$ over $\mathcal E$ which gives a uniform…
We apply random matrix theory to derive spectral density of large sample covariance matrices generated by multivariate VMA(q), VAR(q) and VARMA(q1,q2) processes. In particular, we consider a limit where the number of random variables N and…
We show that quaternionic Gaussian random variables satisfy a generalization of the Wick formula for computing the expected value of products in terms of a family of graphical enumeration problems. When applied to the quaternionic Wigner…
It is well known that the joint probability density of the eigenvalues of Gaussian ensembles of random matrices may be interpreted as a Coulomb gas. We review these classical results for hermitian and complex random matrices, with special…
We exhibit an explicit formula for the spectral density of a (large) random matrix which is a diagonal matrix whose spectral density converges, perturbated by the addition of a symmetric matrix with Gaussian entries and a given (small)…
For general non-Gaussian distributions, the covariance and precision matrices do not encode the independence structure of the variables, as they do for the multivariate Gaussian. This paper builds on previous work to show that for a class…