Abstract:

We study the asymptotic behaviour of the correlation functions of some massless quantum integrable systems. This problem first stated in 1931 in the original paper by H. Bethe is not completely solved but led to many important developments in particular for the asymptotic analysis of Toeplitz and Fredholm determinants. In this talk I’ll present a recent approach based on a number of new hypergeometric identities. These identities closely related to the random partitions theory give the leading terms of the asymptotic for the most interesting (from the physical point of view) two-point correlation functions.