Hydrodynamic Fluctuations

 I will give an introduction to the time-honored theory of hydrodynamic fluctuations. Hydrodynamics – broadly understood as the late-time dynamics of slow excitations – is distinguished by its sparing assumption: thermalization. Its applications are therefore broad and its understanding crucial, in particular for transport in correlated systems. Moreover, this old topic still has surprises in store. I will present two new hydrodynamic phenomena – one that occurs when fluctuations are small: dangerous irrelevance and diffusion cascade – and one that occurs when fluctuations are large: breakdown of diffusion on chiral edges.