Subcritical Contact Process Seen from the Edge: Convergence to   Quasi-Equilibrium
  The subcritical contact process seen from the rightmost infected site has no invariant measures. We prove that nevertheless it converges in distribution to a quasi-stationary measure supported on finite configurations. 
Enrique Andjel, Fran\c{c}ois Ezanno, Pablo Groisman, Leonardo T. Rolla
math.PR