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Fluctuation Moments Induced by Conjugation with Asymptotically Liberating Random Matrix Ensembles
Independent Haar-unitary random matrices and independent Haar-orthogonal random matrices are known to be asymptotically liberating ensembles, and...
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Pseudo-Hermitian Random Matrices
This book is a comprehensive guide to pseudo-Hermitian random matrices, their properties, and their role in many models that are relevant to physical...
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Vector Random Fields on the Probability Simplex with Metric-Dependent Covariance Matrix Functions
This paper constructs a class of isotropic vector random fields on the probability simplex via infinite series expansions involving the...
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Random Walks
We start with the random walk on the 1-d lattice of the integers of the real line. From this simple model we derive the equations for the process of...
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Random Matrix Theory
For the most part, the preceding chapters dealt with large sample techniques under the traditional asymptotic framework, that is, the sample size...
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The Characteristic Polynomial of a Random Matrix
Form an n × n matrix by drawing entries independently from {±1} (or another fixed nontrivial finitely supported distribution in Z ) and let φ be the...
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Continuous Random Vectors
Having studied discrete random variables, that is, random variables taking their values in a finite or countable set, we now introduce random...
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Near-linear convergence of the Random Osborne algorithm for Matrix Balancing
We revisit Matrix Balancing, a pre-conditioning task used ubiquitously for computing eigenvalues and matrix exponentials. Since 1960, Osborne’s...
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Large gap asymptotics on annuli in the random normal matrix model
We consider a two-dimensional determinantal point process arising in the random normal matrix model and which is a two-parameter generalization of...
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Sphericity and Identity Test for High-dimensional Covariance Matrix Using Random Matrix Theory
This paper addresses the issue of testing sphericity and identity of high-dimensional population covariance matrix when the data dimension exceeds...
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Measurement model and accuracy analysis of parabolic ballistic projectile flight parameters based on random matrix
The existing six light screen array measuring methodology of uniform linear trajectory is unable to determine the impact coordinate and flight speed...
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Entanglement of Pseudo-Hermitian Random States
By using an abstract model of pseudo-Hermitian random matrices and Dyson’s scheme to deal with density matrix of non-Hermitian matrix, the...
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HARFE: hard-ridge random feature expansion
We propose a random feature model for approximating high-dimensional sparse additive functions called the hard-ridge random feature expansion method...
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Uncertainty quantification for random domains using periodic random variables
We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random...
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Marchenko–Pastur Law for Spectra of Random Weighted Bipartite Graphs
AbstractWe study the spectra of random weighted bipartite graphs. We establish that, under specific assumptions on the edge probabilities, the...