Self-repulsive walks at critical drifts and wetting transition for DGFF
Vortrag von Prof. Dr. Dmitry Ioffe Datum: 15.09.16 Zeit: 13.30 - 14.20 Raum: Y16G05
I shall discuss two problems, which we tried to solve with Erwin,
and still wish to see them solved.
The first one is about general finite range walks in self-repulsive
potentials. For such walks we can show that there is always a unique
critical drift, and that the
walk is ballistic away from criticality. Sub-ballistic behaviour at
criticality is an open
question. Duminil-Copin and Hammond solved it for the simple
symmetric RW, but their arguments
rely on lattice symmetries in an essential way.
The second problem is about wetting transition for 2D Discrete
Gaussian Free Field. The existence
of such transition was proved by Caputo and Velenik building on
earlier ideas of Chalker. The
proof, however, does not really explains the phenomenon and the nature
of competition
near the transition point, which we tried to understand in terms of
percolation with clustering. It seems that
such an approach leads to an alternative proof of wetting transition
for DGFF on binary trees, or
even for 2D DGFF, with presumably better bounds on
critical pinning strength.