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 75 for “"Matrix theory"”.
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Topics in Combinatorics and Random Matrix Theory
… 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 key …
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Essays in econometrics and random matrix theory
This dissertation develops new econometric procedures for the analysis of high-dimensional datasets commonly encountered in finance, macroeconomics or industrial organization. First, I show that traditional approaches to the estimation of latent factors in financial data underestimate the number of …
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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 hard …
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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
… 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
… (1952) seminal work on Modern Portfolio Theory (MPT) describes a methodology to construct an optimal portfolio of risky stocks. The constructed portfolio is based on a trade-off between risk and reward, and will depend on the risk- return preferences of the investor. Implementation of MPT …
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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
… to existing results in classical random matrix theory over R, C or H, but often exhibit probabilistic behaviors which differ markedly from these known cases. Specifically, we prove the following: (1) We show exact relations between products and corners of random matrices over Qₚ and …
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Spectral Geometry for Deep Learning: Compression and Hallucination Detection via Random Matrix Theory
… 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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Free approximation of transport properties in organic system using Stochastic Random Matrix Theory
… 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 of …
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The development and application of random matrix theory in adaptive signal processing in the sample deficient regime
… 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
… 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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Foundational Investigations & Astronomical Implications of Quantum Gravity
… a background independent formulation of Matrix Theory. We discuss a background independent formulation of a holographic theory of quantum gravity. The present thesis incorporates the necessary background material on geometry of canonical quantum theory, holography and spacetime …
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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 physical …
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A Mathematical Model of Adhesion Interactions between Living Cells
… spherical cells. In addition, several results in matrix theory are proved with the end of showing that the equations produced by the model uniquely determine the motion of the system or cells.
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