Recent developments in the large-N analysis of correlation functions
Karol Kozlowski (Universite de Bourgogne)
Tuesday 9th December, 2014 15:00-16:00 tba
The scalar products and certain correlation functions of models solvable by the quantum separation of variables can be expressed in terms of N-fold multiple integrals which can be thought of as the partition function of a one dimensional gas of particles evolving on a curve C , trapped in an external potential V and interacting through repulsive two-body interactions. The choice of the curve C and of the confining potential V determines a given model. The analysis of the large-N asymptotic behaviour of these integrals is of interest to the description of the continuum limit of the integrable model.
In this talk, I shall report on recent developments in the large-N analysis of such integrals and discuss, on some specific examples, the form taken by the asymptotics. Part of the results that I will present issue from a joint work with G. Borot (Max-Planck Institut, Bonn, Germany) and A. Guionnet (MIT, Boston, USA).