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OverviewThis 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. Full Product DetailsAuthor: Pavel Bleher , Karl LiechtyPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: No. 32 Weight: 0.456kg ISBN: 9781470409616ISBN 10: 1470409615 Pages: 224 Publication Date: 30 April 2014 Audience: Professional and scholarly , College/higher education , Professional and scholarly , Professional & Vocational , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: Temporarily unavailable  The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsReviewsAuthor InformationPavel Bleher, Indiana University-Purdue University Indianapolis, IN, USA Karl Liechty, University of Michigan, Ann Arbor, MI, USA Tab Content 6Author Website:Countries AvailableAll regions |
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