Related papers: On the Correlation Functions of the Characteristic…
We calculate the average of two characteristic polynomials for the real Ginibre ensemble of asymmetric random matrices, and its chiral counterpart. Considered as quadratic forms they determine a skew-symmetric kernel from which all complex…
We establish the asymptotics of the joint moments of the characteristic polynomial of a random unitary matrix and its derivative for general real values of the exponents, proving a conjecture made by Hughes in 2001. Moreover, we give a…
We compute correlation functions of inverse powers and ratios of characteristic polynomials for random matrix models with complex eigenvalues. Compact expressions are given in terms of orthogonal polynomials in the complex plane as well as…
We compute the leading order asymptotic of the maximum of the characteristic polynomial for i.i.d. matrices with real or complex entries. In particular, this result is new even for real Ginibre matrices, which was left as an open problem in…
An elementary derivation of the Borodin-Sinclair-Forrester-Nagao Pfaffian point process, which characterises the law of real eigenvalues for the real Ginibre ensemble in the large matrix size limit, uses the averages of products of…
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…
We establish asymptotic formulae for general joint moments of characteristic polynomials and their higher-order derivatives associated with matrices drawn randomly from the groups $\mathrm{USp}(2N)$ and $\mathrm{SO}(2N)$ in the limit as…
We show that the averaged characteristic polynomial and the averaged inverse characteristic polynomial, associated with Hermitian matrices whose elements perform a random walk in the space of complex numbers, satisfy certain partial…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
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…
We calculate joint moments of the characteristic polynomial of a random unitary matrix from the circular unitary ensemble and its derivative in the case that the power in the moments is an odd positive integer. The calculations are carried…
The eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalised to discrete settings involving either a linear or exponential lattice. The corresponding correlation functions can be expressed…
It is a result of Ginibre that the normalized bulk $k$-point correlation functions of a complex $n\times n$ Gaussian matrix with independent entries of mean zero and unit variance are asymptotically given by the determinantal point process…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
We derive a non-asymptotic expression for the moments of traces of monomials in several independent complex Wishart matrices, extending some explicit formulas available in the literature. We then deduce the explicit expression for the…
We investigate the joint convergence of independent random Toeplitz matrices with complex input entries that have a pair-correlation structure, along with deterministic Toeplitz matrices and the backward identity permutation matrix.…
Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general…
We study the characteristic polynomial $p_{n}(x)=\prod_{j=1}^{n}(|z_{j}|-x)$ where the $z_{j}$ are drawn from the Mittag-Leffler ensemble, i.e. a two-dimensional determinantal point process which generalizes the Ginibre point process. We…
Motivated by the recent work on asymptotic independence relations for random matrices with non-commutative entries, we investigate the limit distribution and independence relations for large matrices with identically distributed and Boolean…
We investigate the spectral distribution of random matrix ensembles with correlated entries. We consider symmetric matrices with real valued entries and stochastically independent diagonals. Along the diagonals the entries may be…