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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/2733

Title: From Wishart to Jacobi ensembles: Statistical properties and applications
Authors: Vivo, Pierpaolo
Advisors: Akemann, G
Publication Date: 2008
Publisher: Brunel University, School of Information Systems, Computing and Mathematics
Abstract: Sixty 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.
Description: This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.
URI: http://bura.brunel.ac.uk/handle/2438/2733
Appears in Collections:School of Information Systems, Computing and Mathematics Research Papers
Mathematical Science
Dept of Mathematics Theses

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