On the genealogy of branching random walks and of directed polymers
arXiv:1607.06610 · doi:10.1209/0295-5075/115/40005
Abstract
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.
7 pages, 3 figures, submitted to EPL