Hardcover ISBN:  9781470409616 
Product Code:  CRMM/32 
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eBook ISBN:  9781470414429 
Product Code:  CRMM/32.E 
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Hardcover ISBN:  9781470409616 
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Product Code:  CRMM/32.B 
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Hardcover ISBN:  9781470409616 
Product Code:  CRMM/32 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
eBook ISBN:  9781470414429 
Product Code:  CRMM/32.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9781470409616 
eBook ISBN:  9781470414429 
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 DetailsCRM Monograph SeriesVolume: 32; 2014; 224 ppMSC: Primary 60; Secondary 82
This book provides a detailed description of the RiemannHilbert 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 sixvertex 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 sixvertex model is an exactly solvable twodimensional model in statistical physics, and thanks to the IzerginKorepin 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 sixvertex model and include a proof of the IzerginKorepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the sixvertex model with domain wall boundary conditions in all the three phases: disordered, ferroelectric, and antiferroelectric.
Titles in this series are copublished with the Centre de recherches mathématiques.
ReadershipGraduate students and research mathematicians interested in random matrices and statistical mechanics.

Table of Contents

Chapters

Unitary matrix ensembles

The RiemannHilbert problem for orthogonal polynomials

Discrete orthogonal polynomials on an infinite lattice

Introduction to the sixvertex model

The IzerginKorepin formula

Disordered phase

Antiferroelectric phase

Ferroelectric phase

Between the phases


Additional Material

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This book provides a detailed description of the RiemannHilbert 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 sixvertex 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 sixvertex model is an exactly solvable twodimensional model in statistical physics, and thanks to the IzerginKorepin 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 sixvertex model and include a proof of the IzerginKorepin formula. Using the RH approach, they explicitly calculate the leading and subleading terms in the thermodynamic asymptotic behavior of the partition function of the sixvertex model with domain wall boundary conditions in all the three phases: disordered, ferroelectric, and antiferroelectric.
Titles in this series are copublished with the Centre de recherches mathématiques.
Graduate students and research mathematicians interested in random matrices and statistical mechanics.

Chapters

Unitary matrix ensembles

The RiemannHilbert problem for orthogonal polynomials

Discrete orthogonal polynomials on an infinite lattice

Introduction to the sixvertex model

The IzerginKorepin formula

Disordered phase

Antiferroelectric phase

Ferroelectric phase

Between the phases