Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 44 for “"random matrices"”.
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Eigenvalues and condition numbers of random matrices
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1989.
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Linear Algebra, Random Matrices and Lie Theory
… Cartan decomposition applied to structured matrices proves the existence of several known matrix factorizations at once and at the same time reveals a number of new matrix factorizations. Finally in the last part we derive the joint eigenvalue-like densities of the classical random matrices …
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Topics in complex random matrices and information theory
… of both central and noncentral complex Wishart matrices are investigated with the objective of studying several open problems in information theory and numerical analysis, etc. Specifically, the largest, kth largest, and the smallest eigenvalue distributions of complex Wishart matrices and the …
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Random matrices, quantum chaos and irreversible classical dynamics
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1996.
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Topics in linear spectral statistics of random matrices
The behavior of the spectrum of a large random matrix is a topic of great interest in probability theory and statistics. At a global level, the limiting spectra of certain random matrix models have been known for some time. For example, the limiting spectral measure of a Wigner matrix is a …
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Quantitative invertibility of random matrices : a combinatorial perspective
… tail behavior of the least singular value of random matrices - a subject which has been intensely studied in the past two decades. Our focus is on obtaining high probability bounds, rather than on estimating the least singular value of a 'typical' realisation of the random matrix. In our main …
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On the computation of probabilities and eigenvalues for random and non-random matrices
… or complex. The eigenvalues of an n-by-n real random matrix whose elements are independent random variables with standard normal are examined. An exact expression to determine the probability Pn,k that exactly k eigenvalues are real are derived in [1]. This expression was used to compute the …
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Characteristic polynomials of random matrices and their role in an effective theory of strong interactions
… on the spectral eigenvalue statistics of random matrix models, with applications in effective field theory models of Quantum chromodynamics (QCD). The symmetries of the field theory lead to random matrix ensembles named chiral Gaussian Unitary Ensemble (chGUE(N)) and extensions thereof. …
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Asymptotic distribution of eigenvalues of random matrices and characterization of the Gaussian distribution by rotational invariance
The study falls in the area of random equations; in particular properties of random matrices have been studied. The dissertation makes precise some statistical theories of spectra developed in recent years by a number of physicists. Two basic results have been achieved. The first result is a …
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Universal Scaling Limits of the Symplectic Elliptic Ginibre Ensemble
… with eigenvalue statistics of non-Hermitian random matrices in the symplectic symmetry class. It contributes to the questions of how to compute the microscopic scaling limit and whether it is universal.
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Random and exact structures in combinatorics
… show several developments related to notions of randomness and structure in combinatorics and probability. One central notion, the pseudorandomness-structure dichotomy, has played a key role in additive combinatorics and extremal graph theory. More generally, however, such notions come into play …
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Applied stochastic eigen-analysis
… the application of the theory of large random matrices to high-dimensional inference problems when the samples are drawn from a multivariate normal distribution. A longstanding problem in sensor array processing is addressed by designing an estimator for the number of signals in white …
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Asymptotics, exact results, and analogies in p-adic random matrix theory
… a compilation of exact results regarding p-adic random matrices and Hall-Littlewood polynomials, and asymptotic results proven using these tools. Many of the results of both types are motivated and guided by analogies to existing results in classical random matrix theory over R, C or H, but often …
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The stochastic operator approach to random matrix theory
Classical random matrix models are formed from dense matrices with Gaussian entries. Their eigenvalues have features that have been observed in combinatorics, statistical mechanics, quantum mechanics, and even the zeros of the Riemann zeta function. However, their eigenvectors are …
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Non commutative version of arithmetic geometric mean inequality and crossed product of ternary ring of operators
… In Chapter 3, we provide some applications from random matrices such as Wishart random matrices, vector-valued moments of convex bodies, and freely independent operators. The second part is about a ternary ring of operators (TRO). After giving a quick survey for the work of Todorov on the …
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Preconditioners constructed from the interpolative decomposition for the variable coefficient Poisson problem
… an idea based on interpolative decomposition and random matrices. We find that this procedure does create an efficient preconditioner to get at the coupling between subdomains.
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The Fourier-Bessel Series and Hard Edge Limits
… kernels are two of the most fundamental in random matrices and growth models more generally. Broadly speaking, one often encounters the Airy kernel when studying models where the relevant eigenvalues or particles are unbounded, and the Bessel kernel when examining their constrained …
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Compressive Sensing
… In this expository, sampling will center on random matrices and expander graphs, while reconstruction will use multiple numerical optimization techniques. Although theoretical performance bounds for these techniques can be found scattered throughout the published literature, there are few …
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Second-order finite free probability
… is a new field lying at the intersection of random matrix theory and non-commutative probability. It is called “finite” because unlike traditional free probability, which takes the perspective of operators on infinite-dimensional vector spaces, finite free probability focuses on the study of …
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Application of RMT-RNN improved decomposition onto defected system
… of a stochastic optimization algorithm - Random Matrix Theory coupled with Neural Networks (RMT-RNN) to large static systems with relatively large disorder in mesoscopic systems. It is a new algorithm that can quickly decompose random matrices with real eigenvalues for further study of …
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