A classical result obtained in the 50’s and 60’s by Bogoliubov, Parasiuk, Hepp and Zimmerman provides a prescription on how to renormalise amplitudes of Feynman diagrams arising in perturbative quantum field theory in a consistent way. We will discuss an analogue of this theorem which has both an analytic and a probabilistic interpretation. In particular, we will see that it implies that the solutions to a large class of nonlinear stochastic PDEs depend on their driving noise in a surprisingly rigid way. This rigidity is a mathematical manifestation of the “universality” taken for granted when building our intuition on the large-scale behaviour of probabilistic models.

**Date**: 10 March 2017, 15:30 (Friday, 8th week, Hilary 2017)**Venue**: Large Lecture Theatre, LG.03**Speaker**: Professor Martin Hairer (University of Warwick)**Organising department**: Department of Statistics**Organiser**: Professor Arnaud Doucet (University of Oxford)**Organiser contact email address**: events@stats.ox.ac.uk**Part of**: Distinguished Speaker Seminar**Booking required?**: Not required**Audience**: Members of the University only**This talk features in the following public collections**:- Editor: Beverley Lane