Skew-orthogonal Polynomials and Random Matrix Theory

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  • Skew-orthogonal Polynomials and Random Matrix Theory Book Detail

  • Author : Saugata Ghosh
  • Release Date : 2009
  • Publisher :
  • Genre : Electronic books
  • Pages : 127
  • ISBN 13 : 9781470417710
  • File Size : 10,10 MB

Skew-orthogonal Polynomials and Random Matrix Theory by Saugata Ghosh PDF Summary

Book Description: Orthogonal polynomials satisfy a three-term recursion relation irrespective of the weight function with respect to which they are defined. This gives a simple formula for the kernel function, known in the literature as the Christoffel-Darboux sum. The availability of asymptotic results of orthogonal polynomials and the simple structure of the Christoffel-Darboux sum make the study of unitary ensembles of random matrices relatively straightforward. In this book, the author develops the theory of skew-orthogonal polynomials and obtains recursion relations which, unlike orthogonal polynomials, de.

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"This book features a unified derivation of the mathematical theory of the three classical types of invariant random matrix ensembles-orthogonal, unitary, and s