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 48 for “"Random Matrix Theory"”.
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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
… (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
… 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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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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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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Correlated trajectories in semiclassical approaches to quantum chaos
… obtain a small $\tau$ expansion that agrees with random matrix theory for systems with and without time reversal symmetry. Then we consider correlations of the Wigner time delay in open systems. We study a form factor $K(\tau,x,y,M)$ that depends on the number of scattering channels $M$, the …
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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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Beta-ensembles with covariance
… the [beta]-MANOVA case. In infinite-dimensional random matrix theory, we find the moments of the Wachter law, and the Jacobi parameters and free cumulants of the McKay and Wachter laws. We also present an algorithm that uses complex analysis to solve "The Moment Problem." It takes the first batch …
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Alternative risk management: correlation and complexity
… using the equal-time cross-correlation matrix. These Complex Systems are characterised by events such as Market Crashes or Seizures, which are associated with periods of hypersynchronisation. In this Thesis, the Risk Characterisation and Reduction of Complex Systems is studied, using the …
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Aspects of Eigenstate Thermalization
… opments have demonstrated the centrality of random matrix theory and free probability to the ETH. This thesis focuses primarily on a version of the ETH known as ergodic bipartition (EB). The fundamental physical result of the EB is that the entanglement entropy of a subsystem is its …
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