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Synopsis
Outlining a connection from random matrices to the six-vertex model of statistical physics, Bleher and Liechty focus on the Riemann-Hilbert method for both continuous and discrete orthogonal polynomials, and applications of this approach to matrix models as well as to the six-vertex model. They cover unitary matrix ensembles, the Riemann-Hilbert problem for orthogonal polynomials, discrete orthogonal polynomials on an infinite lattice, introducing the six-vertex model, the Izergin-Korepin formula, the disordered phase, the anti-ferroelectric phase, the ferroelectric phase, and between the phases. Annotation ©2014 Book News, Inc., Portland, OR (booknews.com)
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About the Author
Pavel Bleher, Indiana University-Purdue University Indianapolis, IN, USAKarl Liechty, University of Michigan, Ann Arbor, MI, USA
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Random Matrices and the Six-Vertex Model
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Random Matrices and the Six-Vertex Model
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Hardback. Condition: New. 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. Seller Inventory # LU-9781470409616
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Random Matrices and the Six-Vertex Model (CRM Monograph, 32)
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Hardback. Condition: New. 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. Seller Inventory # LU-9781470409616
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