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Random Matrices and the Six-Vertex Model
 
Pavel Bleher Indiana University-Purdue University Indianapolis, Indianapolis, IN
Karl Liechty University of Michigan, Ann Arbor, MI
A co-publication of the AMS and Centre de Recherches Mathématiques
Random Matrices and the Six-Vertex Model
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
Random Matrices and the Six-Vertex Model
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Random Matrices and the Six-Vertex Model
Pavel Bleher Indiana University-Purdue University Indianapolis, Indianapolis, IN
Karl Liechty University of Michigan, Ann Arbor, MI
A co-publication of the AMS and Centre de Recherches Mathématiques
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
  • Book Details
     
     
    CRM Monograph Series
    Volume: 322014; 224 pp
    MSC: 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.

    Readership

    Graduate students and research mathematicians interested in random matrices and statistical mechanics.

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 322014; 224 pp
MSC: 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.

Readership

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
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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