Recent exact and asymptotic results for products of independent random matrices

G Akemann, JR Ipsen - arxiv preprint arxiv:1502.01667, 2015‏ - arxiv.org
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 …

Progress on the study of the Ginibre ensembles I: GinUE

SS Byun, PJ Forrester - arxiv preprint arxiv:2211.16223, 2022‏ - arxiv.org
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 …

Progress on the study of the Ginibre ensembles II: GinOE and GinSE

SS Byun, PJ Forrester - arxiv preprint arxiv:2301.05022, 2023‏ - arxiv.org
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 …

Random neural networks in the infinite width limit as Gaussian processes

B Hanin - The Annals of Applied Probability, 2023‏ - projecteuclid.org
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 …

Singular values of products of Ginibre random matrices, multiple orthogonal polynomials and hard edge scaling limits

ABJ Kuijlaars, L Zhang - Communications in Mathematical Physics, 2014‏ - Springer
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 …

Random-matrix models of monitored quantum circuits

VB Bulchandani, SL Sondhi, JT Chalker - Journal of Statistical Physics, 2024‏ - Springer
We study the competition between Haar-random unitary dynamics and measurements for
unstructured systems of qubits. For projective measurements, we derive various properties …

Statistical limits of dictionary learning: random matrix theory and the spectral replica method

J Barbier, N Macris - Physical Review E, 2022‏ - APS
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 …

[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 …

Singular values of products of random matrices and polynomial ensembles

ABJ Kuijlaars, D Stivigny - Random Matrices: Theory and …, 2014‏ - World Scientific
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 …

Singular value statistics of matrix products with truncated unitary matrices

M Kieburg, ABJ Kuijlaars… - International Mathematics …, 2016‏ - academic.oup.com
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 …