abstract: In this talk we are going to survey some methods and results proving stabilization of long-time asymptotics of PDE by noise, in terms of the collapse of the (random) attractor to a single point. We will then lay out some recent results obtained in Gess, JDDE, 2013 where it is shown that the infinite-dimensional attractor of degenerate, perturbed p-Laplace equations collapses if enough additive noise is included.