Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.557680
Title: From Wishart to Jacobi ensembles : statistical properties and applications
Author: Vivo, Pierpaolo
Awarding Body: Brunel University
Current Institution: Brunel University
Date of Award: 2008
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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.
Supervisor: Akemann, G. Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.557680  DOI: Not available
Keywords: Random matrix ; quantum conductance
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