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CRM Monograph Series
2014; 224 pp; hardcover
List Price: US$98
Member Price: US$78.40
Order Code: CRMM/32
Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert 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 Riemann-Hilbert 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 six-vertex 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 six-vertex model is an exactly solvable two-dimensional model in statistical physics, and thanks to the Izergin-Korepin 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 six-vertex model and include a proof of the Izergin-Korepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the six-vertex model with domain wall boundary conditions in all the three phases: disordered, ferroelectric, and antiferroelectric.
Titles in this series are co-published with the Centre de Recherches Mathématiques.
Graduate students and research mathematicians interested in random matrices and statistical mechanics.
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