14:15
We consider a
directed random polymer interacting with an interface
that carries random charges some of which attract while others repel
the polymer. Such a polymer can be in a localized or delocalized
phase, i.e., it stays near the interface or wanders away respectively.
The phase it chooses depends on the temperature and the average bias
of the disorder. At a given temperature, there is a critical bias
separating the two phases. A question of particular interest, and
which has been studied extensively in the Physics and Mathematics
literature, is whether the quenched critical bias differs from the
annealed critical bias. When it does, we say that the disorder is
relevant.
Using a large deviations result proved recently by Birkner, Greven,
and den Hollander, we derive a variational formula for the quenched
critical bias. This
leads to a necessary and sufficient condition for
disorder relevance that implies easily some known results as well as
new ones.
The talk is based on joint work with Frank den Hollander.