On the genealogy of branching random walks and of directed polymers
  It is well known that the mean field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta functions. Here we show that the leading finite size correction to this distribution of overlaps has a universal character which can be computed explicitly. Our results can also be interpreted as genealogical properties of branching Brownian motion or of branching random walks. 
Bernard Derrida and Peter Mottishaw
cond-mat.stat-mech cond-mat.dis-nn