Convergence in distribution for subcritical 2D oriented percolation seen   from its rightmost point
  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. 
E. D. Andjel
math.PR