
Introduction  Preview Material  Table of Contents  Supplementary Material 
CRM Monograph Series 2014; 224 pp; hardcover Volume: 32 ISBN10: 1470409615 ISBN13: 9781470409616 List Price: US$98 Member Price: US$78.40 Order Code: CRMM/32 See also: Orthogonal Polynomials and Random Matrices: A RiemannHilbert Approach  Percy Deift Random Matrix Theory: Invariant Ensembles and Universality  Percy Deift and Dimitri Gioev Eigenvalue Distribution of Large Random Matrices  Leonid Pastur and Mariya Shcherbina  This book provides a detailed description of the RiemannHilbert approach (RH approach) to the asymptotic analysis of both continuous and discrete orthogonal polynomials, and applications to random matrix models as well as to the sixvertex model. The RH approach was an important ingredient in the proofs of universality in unitary matrix models. This book gives an introduction to the unitary matrix models and discusses bulk and edge universality. The sixvertex model is an exactly solvable twodimensional model in statistical physics, and thanks to the IzerginKorepin formula for the model with domain wall boundary conditions, its partition function matches that of a unitary matrix model with nonpolynomial interaction. The authors introduce in this book the sixvertex model and include a proof of the IzerginKorepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the sixvertex model with domain wall boundary conditions in all the three phases: disordered, ferroelectric, and antiferroelectric. Titles in this series are copublished with the Centre de Recherches Mathématiques. Readership Graduate students and research mathematicians interested in random matrices and statistical mechanics. 


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