Related papers: On Painleve Related Functions Arising in Random Ma…
In this paper we study the asymptotic behavior for large argument of a family of solutions of the Painlev\'e equation P$_{\rm VI} arising in the context of Random Matrix Theory [1]. We show this family of solutions are uniquely determined…
This paper is concerned with certain connections between the ensemble of n x n unitary matrices -- specifically the characteristic function of the random variable tr(U) -- and combinatorics -- specifically Ulam's problem concerning the…
In this paper we focus on the finite n probability distribution function of the largest eigenvalue in the classical Gaussian Ensemble of n by n matrices (GEn). We derive the finite n largest eigenvalue probability distribution function for…
The $\tau$-function theory of Painlev\'e systems is used to derive recurrences in the rank $n$ of certain random matrix averages over U(n). These recurrences involve auxilary quantities which satisfy discrete Painlev\'e equations. The…
This is an expository account of the edge eigenvalue distributions in random matrix theory and their application in multivariate statistics. The emphasis is on the Painlev\'e representations of these distributions.
We study the asymptotic behavior of the partition function and the correlation kernel in random matrix ensembles of the form $\frac{1}{Z_n} \big|\det \big( M^2-tI \big)\big|^{\alpha} e^{-n\operatorname{Tr} V(M)}dM$, where $M$ is an $n\times…
This paper first surveys the connection of integrable systems of the Painleve type to various distribution functions appearing in Wigner-Dyson random matrix theory. A short discussion is then given of the appearance of these same…
A feature of certain ensembles of random matrices is that the corresponding measure is invariant under conjugation by unitary matrices. Study of such ensembles realised by matrices with Gaussian entries leads to statistical quantities…
The eigenvalues of an arbitrary quaternionic matrix have a joint probability distribution function first derived by Ginibre. We show that there exists a mapping of this system onto a fermionic field theory and then use this mapping to…
The paper is concerned with the asymptotic behavior of the correlation functions of the characteristic polynomials of non-Hermitian random matrices with independent entries. It is shown that the correlation functions behave like that for…
A recursive method is derived to calculate all eigenvalue correlation functions of a random hermitian matrix in the large size limit, and after smoothing of the short scale oscillations. The property that the two-point function is…
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…
In this paper we focus on the large n probability distribution function of the largest eigenvalue in the Gaussian Orthogonal Ensemble of n by n matrices (GOEn). We prove an Edgeworth type Theorem for the largest eigenvalue probability…
We investigate the universality of singular value and eigenvalue distributions of matrix valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution…
Orthogonal polynomials and multiple orthogonal polynomials are interesting special functions because there is a beautiful theory for them, with many examples and useful applications in mathematical physics, numerical analysis, statistics…
In a recent study of large non-null sample covariance matrices, a new sequence of functions generalizing the GUE Tracy-Widom distribution of random matrix theory was obtained. This paper derives Painlev\'e formulas of these functions and…
We study the partition function from random matrix theory using a well known connection to orthogonal polynomials, and a recently developed Riemann-Hilbert approach to the computation of detailed asymptotics for these orthogonal…
Recent work of Belinschi, Mai and Speicher resulted in a general algorithm to calculate the distribution of any selfadjoint polynomial in free variables. Since many classes of independent random matrices become asymptotically free if the…
The integrable structure of Ginibre's Orthogonal Ensemble of random matrices is looked at through the prism of the probability "p_{n,k}" to find exactly "k" real eigenvalues in the spectrum of an "n" by "n" real asymmetric Gaussian random…
It is now believed that the limiting distribution function of the largest eigenvalue in the three classic random matrix models GOE, GUE and GSE describe new universal limit laws for a wide variety of processes arising in mathematical…