Asymptotic Expansion of a Partition Function Related to the Sinh-model

  • Gaëtan Borot
  • Alice Guionnet
  • Karol K. Kozlowski

Part of the Mathematical Physics Studies book series (MPST)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Gaëtan Borot, Alice Guionnet, Karol K. Kozlowski
    Pages 1-52
  3. Gaëtan Borot, Alice Guionnet, Karol K. Kozlowski
    Pages 53-67
  4. Asymptotic Expansion of Open image in new window—The Schwinger–Dyson Equation Approach
    Gaëtan Borot, Alice Guionnet, Karol K. Kozlowski
    Pages 69-98
  5. Gaëtan Borot, Alice Guionnet, Karol K. Kozlowski
    Pages 99-131
  6. Gaëtan Borot, Alice Guionnet, Karol K. Kozlowski
    Pages 133-164
  7. Gaëtan Borot, Alice Guionnet, Karol K. Kozlowski
    Pages 165-192
  8. Back Matter
    Pages 193-222

About this book


This book elaborates on the asymptotic behaviour, when N is large, of certain N-dimensional integrals which typically occur in random matrices, or in 1+1 dimensional quantum integrable models solvable by the quantum separation of variables. The introduction presents the underpinning motivations for this problem, a historical overview, and a summary of the strategy, which is applicable in greater generality. The core  aims at proving an expansion up to o(1) for the logarithm of the partition function of the sinh-model. This is achieved by a combination of potential theory and large deviation theory so as to grasp the leading asymptotics described by an equilibrium measure, the Riemann-Hilbert approach to truncated Wiener-Hopf in order to analyse the equilibrium measure, the Schwinger-Dyson equations and the boostrap method to finally obtain an expansion of correlation functions and the one of the partition function. This book is addressed to researchers working in random matrices, statistical physics or integrable systems, or interested in recent developments of asymptotic analysis in those fields.


Schwinger-Dyson equation Riemann-Hilbert problem Gaussian potential concentration of measure loop equations KPZ models Toda lattice six-vertex model XXZ chains algebraic Bethe Ansatz quantum Toda chain Selberg integral separation of variables quantum separation of variables random matrix theory

Authors and affiliations

  • Gaëtan Borot
    • 1
  • Alice Guionnet
    • 2
  • Karol K. Kozlowski
    • 3
  1. 1.Max Planck Institut für MathematikBonnGermany
  2. 2.Department of MathematicsMITCambridgeUSA
  3. 3.ENS de LyonLaboratoire de Physique-UMR 5672 du CNRSLyonFrance

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-33378-6
  • Online ISBN 978-3-319-33379-3
  • Series Print ISSN 0921-3767
  • Series Online ISSN 2352-3905
  • Buy this book on publisher's site
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