相关论文: Asymptotic normality for traces of polynomials in …
We introduce a family of matrices with non-commutative entries that generalize the classical real Wishart matrices. With the help of the Brauer product, we derive a non-asymptotic expression for the moments of traces of monomials in such…
We present an exact formula for moments and cumulants of several real compound Wishart matrices in terms of an Euler characteristic expansion, similar to the genus expansion for complex random matrices. We consider their asymptotic values…
By using a symbolic method, known in the literature as the classical umbral calculus, the trace of a non-central Wishart random matrix is represented as the convolution of the trace of its central component and of a formal variable…
We prove that any non commutative polynomial of r independent copies of Wigner matrices converges a.s. towards the polynomial of r free semicircular variables in operator norm. This result extends a previous work of Haagerup and…
We examine the asymptotics of the moments of characteristic polynomials of $N\times N$ matrices drawn from the Hermitian ensembles of Random Matrix Theory, in the limit as $N\to\infty$. We focus in particular on the Gaussian Unitary…
In the paper we develop an approach to asymptotic normality through factorial cumulants. Factorial cumulants arise in the same manner from factorial moments, as do (ordinary) cumulants from (ordinary) moments. Another tool we exploit is a…
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…
It is shown that a Wishart matrix of standard complex normal random variables is asymptotically freely independent of an independent random matrix, under minimal conditions, in two different sense of asymptotic free independence.
In this article we study the large $N$ asymptotics of complex moments of the absolute value of the characteristic polynomial of a $N\times N$ complex Ginibre random matrix with the characteristic polynomial evaluated at a point in the unit…
Using new combinatorial techniques, we significantly improve the previous results on asymptotic distributions and asymptotic free independence relations of partial transposes of Wishart random matrices. In particular, we give a necessary…
Based on the multivariate saddle point method we study the asymptotic behavior of the characteristic polynomials associated to Wishart type random matrices that are formed as products consisting of independent standard complex Gaussian and…
We study asymptotics of traces of (noncommutative) monomials formed by images of certain elements of the universal enveloping algebra of the infinite-dimensional unitary group in its Plancherel representations. We prove that they converge…
Keating and Snaith showed that the $2k^{th}$ absolute moment of the characteristic polynomial of a random unitary matrix evaluated on the unit circle is given by a polynomial of degree $k^2$. In this article, uniform asymptotics for the…
Using asymptotics of Toeplitz+Hankel determinants, we establish formulae for the asymptotics of the moments of the moments of the characteristic polynomials of random orthogonal and symplectic matrices, as the matrix-size tends to infinity.…
We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide…
We study the moments of the absolute characteristic polynomial of the real elliptic ensemble, including the case of the real Ginibre ensemble. We obtain asymptotics for all integral moments inside the real bulk to order 1 + o(1). In…
We study moments of characteristic polynomials of truncated Haar distributed matrices from the three classical compact groups O(N), U(N) and Sp(2N). For finite matrix size we calculate the moments in terms of hypergeometric functions of…
Appropriately normalized square random Vandermonde matrices based on independent random variables with uniform distribution on the unit circle are studied. It is shown that as the matrix sizes increases without bound, with respect to the…
Starting from Montgomery's conjecture, there has been a substantial interest on the connections of random matrix theory and the theory of L-functions. In particular, moments of characteristic polynomials of random matrices have been…
The paper is concerned with the correlation functions of the characteristic polynomials of random matrices with independent complex entries. We investigate how the asymptotic behavior of the correlation functions depends on the second…