Studies of non-equilibrium fluctuations have held a center stage during the past few decades of the development of non-equilibrium statistical mechanics. Macroscopic fluctuations display some universal behaviour, quantified by large deviation functions.

In this talk, we describe a few results for non-equilibrium large deviations. In particular, we shall use techniques of integrable probabilities to derive an exact formula for the distribution of a tracer particle in the symmetric exclusion process, thus answering a problem that had eluded solution for decades.

Joint work with Takashi Imamura (Chiba) and Tomohiro Sasamoto (Tokyo).