This project aims at studying a the large-N behaviour of class of integrals over N variables in strong interactions.
Such integrals allow to express various kinds of quantities appearing in mathematical physics, for instance
the correlation functions in the N-site discretisation of the 1+1 dimensional quantum Sinh-Gordon model in finite volume. In fact, on the one hand these integrals generalise rather naturally those describing the integration over the spectrum of large random hermitian matrices while on the other one they bring into the game many new features. The study of their large-N behaviour will allow to obtain a thorough and non-perturbative characterisation of a quantum field theory in finite volume. Moreover, the complete understanding of this problem would allow for an important
progress in mathematics which would pave the way to the large-N analysis of new types of integrals involving integration variables in strong interaction and generalising the famous Coulomb gas models.