Title: From duality to determinants.

Ivan Corwin (Clay Mathematics Institute, MIT and Microsoft Research)

Abstract: I will explain duality for the asymmetric simple exclusion process and then solve the associated quantum many body problem for special initial conditions via a contour integral ansatz. Using the resulting formulas I develop generating series which identify particle location distributions and which can be expressed as Fredholm determinants (one of which coincides with the  Tracy-Widom ASEP formula). Asymptotics of such expressions are readily computable and lead to Kardar-Parisi-Zhang universality class fluctuations. In essence, this is a rigorous discrete deformation of the physicist's (famously non-rigorous) polymer replica trick. This is based on joint work with Alexei Borodin and Tomohiro Sasamoto.