Markovianity and ergodicity for a surface growth PDE
  The paper analyses a model in surface growth, where uniqueness of weak solutions seems to be out of reach. We provide the existence of a weak martingale solution satisfying energy inequalities and having the Markov property. Furthermore, under non-degeneracy conditions on the noise, we establish that any such solution is strong Feller and has a unique invariant measure. 
D. Bl\"omker, F. Flandoli, M. Romito