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CRM Monograph Series 2009; 127 pp; hardcover Volume: 28 ISBN10: 082184878X ISBN13: 9780821848784 List Price: US$51 Member Price: US$40.80 Order Code: CRMM/28 See also: Orthogonal Polynomials and Random Matrices: A RiemannHilbert Approach  Percy Deift Random Matrix Theory: Invariant Ensembles and Universality  Percy Deift and Dimitri Gioev WINWomen in Numbers: Research Directions in Number Theory  AlinaCarmen Cojocaru, Kristin Lauter, Rachel Pries and Renate Scheidler  Orthogonal polynomials satisfy a threeterm 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 ChristoffelDarboux sum. The availability of asymptotic results of orthogonal polynomials and the simple structure of the ChristoffelDarboux sum make the study of unitary ensembles of random matrices relatively straightforward. In this book, the author develops the theory of skeworthogonal polynomials and obtains recursion relations which, unlike orthogonal polynomials, depend on weight functions. After deriving reduced expressions, called the generalized ChristoffelDarboux formulas (GCD), he obtains universal correlation functions and nonuniversal level densities for a wide class of random matrix ensembles using the GCD. The author also shows that once questions about higher order effects are considered (questions that are relevant in different branches of physics and mathematics) the use of the GCD promises to be efficient. Titles in this series are copublished with the Centre de Recherches Mathématiques. Readership Research mathematicians interested in random matrix theory. 


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