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 67 for “"random matrix"”.
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Topics in Combinatorics and Random Matrix Theory
… of enumerative/algebraic combinatorics and random matrix theory. We begin with an expository account of the increasing subsequence problem, contextualizing it as an ``exactly solvable'' Ramsey-type problem and introducing the RSK correspondence. New proofs and generalizations of some of the …
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Essays in econometrics and random matrix theory
… the estimation of discrete choice models with random coe±cients and shows that ignoring individual taste heterogeneity can lead to misleading policy counterfactuals.
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Operators and special functions in random matrix theory
… arise in probabilistic calculations in Random Matrix Theory. These were extensively studied by Tracy and Widom, so we refer to them as Tracy–Widom operators. We prove that the integral operator with Jacobi kernel converges in trace norm to the integral operator with Bessel kernel under a …
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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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Stability-based, random matrix theory filtering of financial portfolios
… describes research on filtering methods using RandomMatrix Theory (RMT) Models in financial markets. In particular, a novel, stability-based RMT filter is proposed and its potential, for reducing stock portfolio risk, is compared to two well-known alternatives. In terms of performance, the …
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Portfolio selection using Random Matrix theory and L-Moments
… the sample mean vector and variance-covariance matrix have been used for this purpose. However, estimation errors result in the optimised portfolios performing poorly out-of-sample. This dissertation considers two approaches to obtaining a more robust estimate of the variance-covariance matrix. …
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Efficient estimation for Markowitz's portfolio optimization by using random matrix theory
In this thesis, we first prove that under some situations the traditional (plug-in) return for the MV optimization is square of gamma times bigger than the theoretical optimal return, while under situations, the plug-in return is bigger than but may not be same times larger than its theoretic value …
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Application of Regime Switching and Random Matrix Theory for Portfolio Optimization
… portfolio management of filtering the covariance matrix using Random Matrix Theory (RMT). While it is found that filtering the variance-covariance matrix using Marchenko-Pasteur bounds of RMT improves optimal portfolio choice in both non-regime and regime dependent cases, remarkably in the latter …
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Applications of Random Matrix Theory to Portfolio Management and Financial Networks
This thesis is an application of Random Matrix Theory (RMT) to portfolio management and financial networks. From a portfolio management perspective, we apply the RMT approach to clean measurement noise from correlation matrices constructed for large portfolios of stocks of the FTSE 100. We apply …
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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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Spectral Geometry for Deep Learning: Compression and Hallucination Detection via Random Matrix Theory
… a unifying spectral framework, grounded in Random Matrix Theory (RMT), to address both reliability and efficiency in modern AI systems. First, it introduces EigenTrack, a real-time detector of hallucination and distributional shift in large language and vision-language models. By extracting …
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Sturm sequences and the eigenvalue distribution of the beta-Hermite random matrix ensemble
… derivation of eigenvalue distributions of random matrix ensembles. We first explore the use of Sturm sequences to efficiently compute histograms of eigenvalues for symmetric tridiagonal matrices and apply these ideas to random matrix ensembles such as the [beta]-Hermite ensemble. Using our …
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Free approximation of transport properties in organic system using Stochastic Random Matrix Theory
… a study and application of Stochastic analysis- Random Matrix Theory(RMT) to fast calculate the transport properties of large static systems with relatively large disorder in mesoscopic size. As a major topic of Random Matrix Theory(RMT), free convolution managed to approximate the distribution …
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The development and application of random matrix theory in adaptive signal processing in the sample deficient regime
… processing in the sample deficient regime using random matrix theory. The scenarios in which the sample deficient regime arises include, among others, the cases where the number of observations available in a period over which the channel can be approximated as timeinvariant is limited (wireless …
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The development and application of random matrix theory in adaptive signal processing in the sample deficient regime
… processing in the sample deficient regime using random matrix theory. The scenarios in which the sample deficient regime arises include, among others, the cases where the number of observations available in a period over which the channel can be approximated as time-invariant is limited (wireless …
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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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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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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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Group integrals in chaotic quantum systems
… the generalization of Bessel functions to matrix and supermatrix spaces. Thereby we derive exact expressions for the one and two--point eigenvalue correlator of a random matrix model. The model consists of a sum of two random matrices. One of them is diagonal and models the regular part. …
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Eigenvalue statistics for beta-ensembles
Random matrix theory is a maturing discipline with decades of research in multiple fields now beginning to converge. Experience has shown that many exact formulas are available for certain matrices with real, complex, or quaternion entries. In random matrix jargon, these are the cases β = 1, 2 and …
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