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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.

preprint2016arXivOpen access
Bernard DerridaPeter Mottishaw
cond-mat.stat-mechcond-mat.dis-nn
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Bernard DerridaPeter Mottishaw

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