D. Andjel, E., Convergence in distribution for subcritical 2D oriented percolation seen from its rightmost point, Annals of probability , 42(3), 2014, pp. 1285-1296
We study subcritical two-dimensional oriented percolation seen from its rightmost point on the set of infinite configurations which are bounded above. This a Feller process whose state space is not compact and has no invariant measures. We prove that it converges in distribution to a measure which charges only finite configurations.