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About this product
- DescriptionThis 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.
- Author BiographyGaetan Borot graduated at ENS Paris in theoretical physics, did his PhD at CEA Saclay, and is now a W2 Group Leader at the Max Planck Institute for Mathematics in Bonn. He was also a visiting scholar at MIT, collaborating with Alice Guionnet on the asymptotic analysis of random matrix models. He is working on the mathematical aspects of geometry and physics, ranging from statistical physics, random matrices, integrable systems, enumerative geometry, topological quantum field theories, etc. Alice Guionnet is Director of research CNRS at Ecole Normale Superieure (ENS) Lyon, from MIT where she served as a professor in 2012-2015. She received the MS from ENS Paris in 1993 and the PhD, under the guidance of G. Ben Arous at Universite Paris Sud in 1995. /div>A. Guionnet is a world leading probabilist, working on a program related to operator algebra theory and mathematical physics. She has made important contributions in random matrix theory, including large deviations, topological expansions, but also more classical study of their spectrum and eigenvectors. From 2006-2011 she served as Editor-in-Chief of Annales de L'Institut Henri Poincare (currently on its editorial board), and also serves on the editorial board of Annals of Probability.She has given two Plenary talks and a number of Invited Talks at international meetings, including ICM. Her distinctions include the Miller Institute Fellowship, (2006), the Loeve Prize (2009), the Silver Medal of CNRS (2010) and Simon Investigator (2012). Karol Kajetan Kozlowski is a CNRS Charge de recherche at the Ecole Normale Superieure (ENS) Lyon. He graduated from ENS-Lyon in 2005 and did his PhD at the Laboratoire Physique of ENS-Lyon. He was then a post-doctoral fellow at the Deutsches Elektronen-Synchrotron. His main research interest concern quantum integrable models and various aspects of asymptotic analysis.
- Author(s)Alice Guionnet,Gaetan Borot,Karol K. Kozlowski
- PublisherSpringer International Publishing AG
- Date of Publication16/12/2016
- SubjectScience & Mathematics: Textbooks & Study Guides
- Series TitleMathematical Physics Studies
- Place of PublicationCham
- Country of PublicationSwitzerland
- ImprintSpringer International Publishing AG
- Content Note4 black & white illustrations, biography
- Weight526 g
- Width155 mm
- Height235 mm
- Spine14 mm
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