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dc.contributor.advisorAkemann, G-
dc.contributor.authorVivo, Pierpaolo-
dc.descriptionThis thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.-
dc.description.abstractSixty years after the works of Wigner and Dyson, Random Matrix Theory still remains a very active and challenging area of research, with countless applications in mathematical physics, statistical mechanics and beyond. In this thesis, we focus on rotationally invariant models where the requirement of independence of matrix elements is dropped. Some classical examples are the Jacobi and Wishart-Laguerre (or chiral) ensembles, which constitute the core of the present work. The Wishart-Laguerre ensemble contains covariance matrices of random data, and represents a very important tool in multivariate data analysis, with recent applications to finance and telecommunications. We will first consider large deviations of the maximum eigenvalue, providing new analytical results for its large N behavior, and then a power-law deformation of the classical Wishart-Laguerre ensemble, with possible applications to covariance matrices of financial data. For the Jacobi matrices, which arise naturally in the quantum conductance problem, we provide analytical formulas for quantities of interest for the experiments.en
dc.format.extent1192492 bytes-
dc.publisherBrunel University, School of Information Systems, Computing and Mathematicsen
dc.relation.hasversionJ. Phys. A: Math. Theor. 40(16), 4317 (2007).en
dc.relation.hasversionJ. Phys. A: Math. Theor. 41(12), 122004 (2008).en
dc.relation.hasversionJ. Stat. Mech. (2008) P09002en
dc.subject.otherRandom matrixen
dc.subject.otherQuantum conductanceen
dc.titleFrom Wishart to Jacobi ensembles: Statistical properties and applicationsen
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Dept of Mathematics Theses
Mathematical Sciences

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