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

Gaëtan 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 École Normale Supérieure (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 Université Paris Sud in 1995.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 Poincaré (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 Loève Prize (2009), the Silver Medal of CNRS (2010) and Simon Investigator (2012). Karol Kajetan Kozlowski is a CNRS Chargé de recherche at the École Normale Supérieure (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.

Introduction.- Main results and strategy of proof.- Asymptotic expansion of ln ZN[V], the Schwinger-Dyson equation approach.- The Riemann-Hilbert approach to the inversion of SN.- The operators WN and U-1N.- Asymptotic analysis of integrals.- Several theorems and properties of use to the analysis.- Proof of Theorem 2.1.1.- Properties of the N-dependent equilibrium measure.- The Gaussian potential.- Summary of symbols.

"The main task of the book is to develop an effective method to obtain asymptotic expansions for certain rescaled multiple integrals. ... The book contains five appendices which complement the main results obtained. The 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." (Horacio Grinberg, Mathematical Reviews, August, 2017)