Related papers: The Beta-Wishart Ensemble
The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.
We study the hole propagator of the Calogero-Sutherland model with SU(2) internal symmetry. We obtain the exact expression for arbitrary non-negative integer coupling parameter $\beta$ and prove the conjecture proposed by one of the…
For a not-necessarily commutative ring R we define an abelian group W(R;M) of Witt vectors with coefficients in an R-bimodule M. These groups generalize the usual big Witt vectors of commutative rings and we prove that they have analogous…
We describe the integral equivariant cohomology ring of a weighted projective space in terms of piecewise polynomials, and thence by generators and relations. We deduce that the ring is a perfect invariant, and prove a Chern class formula…
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…
We develop certain combinatorial tools for the study of discriminants of general systems of polynomial equations. Applying these tools in a sequel paper, we completely classify components of such discriminants, generalizing the classical…
We set out the general theory of ``Beck modules'' in a variety of algebras and describe them as modules over suitable ``universal enveloping'' unital associative algebras. We develop a theory of ``noncommutative partial differentiation'' to…
For any lattice polytope $P$, we consider an associated polynomial $\bar{\delta}_{P}(t)$ and describe its decomposition into a sum of two polynomials satisfying certain symmetry conditions. As a consequence, we improve upon known…
We study the diffusion of complex Wishart matrices and derive a partial differential equation governing the behavior of the associated averaged characteristic polynomial. In the limit of large size matrices, the inverse Cole-Hopf transform…
We investigate the universality of microscopic eigenvalue correlations for Random Matrix Theories with the global symmetries of the QCD partition function. In this article we analyze the case of real valued chiral Random Matrix Theories…
This paper revisits the Bayesian CMA-ES and provides updates for normal Wishart. It emphasizes the difference between a normal and normal inverse Wishart prior. After some computation, we prove that the only difference relies surprisingly…
We show that the random matrix theory with non-integer "symmetry parameter" beta describes the statistics of transport parameters of strongly disordered two dimensional systems.
We generalise the finite biquandle colouring invariant to a polynomial invariant based on labelling a knot diagram with a finite birack that reduces to the biquandle colouring invariant in that case. The polynomial is an invariant of a…
The structure function of a random matrix ensemble can be specified as the covariance of the linear statistics $\sum_{j=1}^N e^{i k_1 \lambda_j}$, $\sum_{j=1}^N e^{-i k_2 \lambda_j}$ for Hermitian matrices, and the same with the eigenvalues…
We establish an equivariant quantum Giambelli formula for partial flag varieties. The answer is given in terms of a specialization of universal double Schubert polynomials. Along the way, we give new proofs of the presentation of the…
In this paper one extends the binomial and trinomial coefficients to the concept of 'k-nomial' coefficients, and one obtains some properties of these. As an application one generalizes Pascal's triangle.
In the present paper, by extending some fractional calculus to the framework of Cliffors analysis, new classes of wavelet functions are presented. Firstly, some classes of monogenic polynomials are provided based on 2-parameters weight…
We introduced a generalized Wishart distribution, namely, the Kotz-Wishart distribution. Several existing results based on the normality assumption have been extended. Inspired by the particular form of the pdf of the Kotz-Wishart matrix,…
Consider a doubly-infinite array of iid centered variables with moment conditions, from which one can extract a finite number of rectangular, overlapping submatrices, and form the corresponding Wishart matrices. We show that under basic…
We show how the replica method can be used to compute the asymptotic eigenvalue spectrum of a real Wishart product matrix. For unstructured factors, this provides a compact, elementary derivation of a polynomial condition on the Stieltjes…