Special sessions

A three day short course (18, 19 and 20/2/2026 at P3.10@Técnico and online) by

Claudio Landim, IMPA
Nonequilibrium fluctuations of interacting particle systems

We review recent results on the fluctuations of a reaction-diffusion model. We consider a one-dimensional dynamics obtained as a superposition of a Glauber and a Kawasaki dynamics. The reaction term is tuned so that a dynamical phase transition occurs in the model as a suitable parameter is varied. We study dynamical fluctuations of the density field at the critical point.

We characterise the slowdown of the dynamics at criticality, and prove that this slowdown is induced by a single observable, the global density (or magnetisation). We show that magnetisation fluctuations are non-Gaussian and characterise their limit as the solution of a non-linear SDE. We prove, furthermore, that other observables remain fast: the density field acting on the fast modes (i.e. on mean-0 test functions) and with Gaussian scaling converges, in the sense of finite dimensional distributions, to a Gaussian field with space-time covariance that we compute explicitly.

Permanent link to this information: https://pmp.math.tecnico.ulisboa.pt/lecture_series?sgid=113