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Progress on the study of the Ginibre ensembles I: GinUE
The Ginibre unitary ensemble (GinUE) consists of $ N\times N $ random matrices with
independent complex standard Gaussian entries. This was introduced in 1965 by Ginbre …
independent complex standard Gaussian entries. This was introduced in 1965 by Ginbre …
[كتاب][B] Progress on the Study of the Ginibre Ensembles
SS Byun, PJ Forrester - 2025 - library.oapen.org
This open access book focuses on the Ginibre ensembles that are non-Hermitian random
matrices proposed by Ginibre in 1965. Since that time, they have enjoyed prominence within …
matrices proposed by Ginibre in 1965. Since that time, they have enjoyed prominence within …
Limits and fluctuations of p-adic random matrix products
We show that singular numbers (also known as elementary divisors, invariant factors or
Smith normal forms) of products and corners of random matrices over Q _p Q p are …
Smith normal forms) of products and corners of random matrices over Q _p Q p are …
From integrable to chaotic systems: Universal local statistics of Lyapunov exponents
From integrable to chaotic systems: Universal local statistics of Lyapunov exponents -
IOPscience Skip to content IOP Science home Accessibility Help Search Journals Journals list …
IOPscience Skip to content IOP Science home Accessibility Help Search Journals Journals list …
Gaussian fluctuations for products of random matrices
We study global fluctuations for singular values of $ M $-fold products of several right-
unitarily invariant $ N\times N $ random matrix ensembles. As $ N\to\infty $, we show the …
unitarily invariant $ N\times N $ random matrix ensembles. As $ N\to\infty $, we show the …
Exact relation between singular value and eigenvalue statistics
We use classical results from harmonic analysis on matrix spaces to investigate the relation
between the joint densities of the singular values and the eigenvalues for complex random …
between the joint densities of the singular values and the eigenvalues for complex random …
Universality of local spectral statistics of products of random matrices
We derive exact analytical expressions for correlation functions of singular values of the
product of M Ginibre matrices of size N in the double scaling limit M, N→∞. The singular …
product of M Ginibre matrices of size N in the double scaling limit M, N→∞. The singular …
Correlation functions between singular values and eigenvalues
Exploiting the explicit bijection between the density of singular values and the density of
eigenvalues for bi-unitarily invariant complex random matrix ensembles of finite matrix size …
eigenvalues for bi-unitarily invariant complex random matrix ensembles of finite matrix size …
Polynomial ensembles and Pólya frequency functions
We study several kinds of polynomial ensembles of derivative type which we propose to call
Pólya ensembles. These ensembles are defined on the spaces of complex square, complex …
Pólya ensembles. These ensembles are defined on the spaces of complex square, complex …
Harmonic analysis for rank-1 randomised Horn problems
The randomised Horn problem, in both its additive and multiplicative versions, has recently
drawn an increasing interest. Especially, closed analytical results have been found for the …
drawn an increasing interest. Especially, closed analytical results have been found for the …