Abstract: The Landau equation is a nonlinear PDE, which is equivalent to a nonlinear SDE with unbounded and non-Lipschitz coefficients. This equation arises as a model of the distribution of velocities in a spatially homogeneous gas in a `grazing collision’ limit. The talk will present some probabilistic aspects of a recent work, jointly with Prof. Nicolas Fournier: I will discuss uniqueness and stability via a coupling argument and instantaneous regularisation by noise.