

Hardcover ISBN: | 978-1-4704-0961-6 |
Product Code: | CRMM/32 |
List Price: | $130.00 |
MAA Member Price: | $117.00 |
AMS Member Price: | $104.00 |
eBook ISBN: | 978-1-4704-1442-9 |
Product Code: | CRMM/32.E |
List Price: | $125.00 |
MAA Member Price: | $112.50 |
AMS Member Price: | $100.00 |
Hardcover ISBN: | 978-1-4704-0961-6 |
eBook: ISBN: | 978-1-4704-1442-9 |
Product Code: | CRMM/32.B |
List Price: | $255.00 $192.50 |
MAA Member Price: | $229.50 $173.25 |
AMS Member Price: | $204.00 $154.00 |


Hardcover ISBN: | 978-1-4704-0961-6 |
Product Code: | CRMM/32 |
List Price: | $130.00 |
MAA Member Price: | $117.00 |
AMS Member Price: | $104.00 |
eBook ISBN: | 978-1-4704-1442-9 |
Product Code: | CRMM/32.E |
List Price: | $125.00 |
MAA Member Price: | $112.50 |
AMS Member Price: | $100.00 |
Hardcover ISBN: | 978-1-4704-0961-6 |
eBook ISBN: | 978-1-4704-1442-9 |
Product Code: | CRMM/32.B |
List Price: | $255.00 $192.50 |
MAA Member Price: | $229.50 $173.25 |
AMS Member Price: | $204.00 $154.00 |
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Book DetailsCRM Monograph SeriesVolume: 32; 2014; 224 ppMSC: Primary 60; Secondary 82
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.
ReadershipGraduate students and research mathematicians interested in random matrices and statistical mechanics.
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Table of Contents
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Chapters
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Unitary matrix ensembles
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The Riemann-Hilbert problem for orthogonal polynomials
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Discrete orthogonal polynomials on an infinite lattice
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Introduction to the six-vertex model
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The Izergin-Korepin formula
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Disordered phase
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Antiferroelectric phase
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Ferroelectric phase
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Between the phases
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Additional Material
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RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
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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.
-
Chapters
-
Unitary matrix ensembles
-
The Riemann-Hilbert problem for orthogonal polynomials
-
Discrete orthogonal polynomials on an infinite lattice
-
Introduction to the six-vertex model
-
The Izergin-Korepin formula
-
Disordered phase
-
Antiferroelectric phase
-
Ferroelectric phase
-
Between the phases