### An interacting particle system related to the quantum Toda chain

**O'Connell, N ***(University of Warwick)*

Tuesday 18 September 2012, 15:00-15:40

Meeting Room 4, CMS

#### Abstract

I will describe an interacting particle system which can be `solved' via a connection with the quantum Toda chain. The particle system can be regarded as a discretisation of the KPZ (or stochastic heat) equation and is closely related to a semi-discrete directed random polymer model in 1+1 dimensions. The connection to the quantum Toda chain yields an explicit integral formula for the Laplace transform of the distribution of the partition function associated with the polymer model.