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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 …
A big data architecture design for smart grids based on random matrix theory
Model-based analysis tools, built on assumptions and simplifications, are difficult to handle
smart grids with data characterized by volume, velocity, variety, and veracity (ie, 4Vs data) …
smart grids with data characterized by volume, velocity, variety, and veracity (ie, 4Vs data) …
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 …
Contrasting random and learned features in deep Bayesian linear regression
Understanding how feature learning affects generalization is among the foremost goals of
modern deep learning theory. Here, we study how the ability to learn representations affects …
modern deep learning theory. Here, we study how the ability to learn representations affects …
Exact marginal prior distributions of finite Bayesian neural networks
Bayesian neural networks are theoretically well-understood only in the infinite-width limit,
where Gaussian priors over network weights yield Gaussian priors over network outputs …
where Gaussian priors over network weights yield Gaussian priors over network outputs …
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 …
A novel data-driven situation awareness approach for future grids—Using large random matrices for big data modeling
Data-driven approaches, when tasked with situation awareness, are suitable for complex
grids with massive datasets. It is a challenge, however, to efficiently turn these massive …
grids with massive datasets. It is a challenge, however, to efficiently turn these massive …
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 …