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Recent exact and asymptotic results for products of independent random matrices
In this review we summarise recent results for the complex eigenvalues and singular values
of finite products of finite size random matrices, their correlation functions and asymptotic …
of finite products of finite size random matrices, their correlation functions and asymptotic …
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 …
Progress on the study of the Ginibre ensembles II: GinOE and GinSE
This is part II of a review relating to the three classes of random non-Hermitian Gaussian
matrices introduced by Ginibre in 1965. While part I restricted attention to the GinUE (Ginibre …
matrices introduced by Ginibre in 1965. While part I restricted attention to the GinUE (Ginibre …
Random neural networks in the infinite width limit as Gaussian processes
This article gives a new proof that fully connected neural networks with random weights and
biases converge to Gaussian processes in the regime where the input dimension, output …
biases converge to Gaussian processes in the regime where the input dimension, output …
Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits
Abstract Akemann, Ipsen and Kieburg recently showed that the squared singular values of
products of M rectangular random matrices with independent complex Gaussian entries are …
products of M rectangular random matrices with independent complex Gaussian entries are …
Random-matrix models of monitored quantum circuits
We study the competition between Haar-random unitary dynamics and measurements for
unstructured systems of qubits. For projective measurements, we derive various properties …
unstructured systems of qubits. For projective measurements, we derive various properties …
Statistical limits of dictionary learning: random matrix theory and the spectral replica method
We consider increasingly complex models of matrix denoising and dictionary learning in the
Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank …
Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank …
[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 …
Singular values of products of random matrices and polynomial ensembles
Akemann, Ipsen, and Kieburg showed recently that the squared singular values of a product
of M complex Ginibre matrices are distributed according to a determinantal point process …
of M complex Ginibre matrices are distributed according to a determinantal point process …
Singular value statistics of matrix products with truncated unitary matrices
We prove that the squared singular values of a fixed matrix multiplied with a truncation of a
Haar distributed unitary matrix are distributed by a polynomial ensemble. This result is …
Haar distributed unitary matrix are distributed by a polynomial ensemble. This result is …