This seminar will be presented in hybrid mode.  The speaker will deliver his talk in person.

Title: Multiscale coupling of $P(\phi)_2$ models and the law of the maximum

Abstract: In this talk I will describe results obtained in joint work with Nikolay Barashkov and Michael Hofstetter concerning a coupling between $P(\phi)$ models and the GFF on the two-dimensional torus at all spatial scales. This coupling is based on Polchinski renormalisation group dynamics and can be used to study global probabilistic properties of the $P(\phi)$ model. I will talk about one such application: showing that the law of the maximum converges to a randomly shifted Gumbel distribution, as it does for the GFF. For non-Gaussian fields previous results in this direction have been restricted to the sine-Gordon model, for which there are explicit expansion methods available. No such methods are known to apply to general $P(\phi)$ models. I will describe how we develop a more robust approach to Polchinski renormalisation group based upon stochastic variational methods and discrete harmonic analysis.

The talk will be followed by refreshments in the Huxley Common Room at 5pm.