Konferenz: Workshop on the occasion of Erwin Bolthausen's 70th birthday


Self-repulsive walks at critical drifts and wetting transition for DGFF

{{_Ltalk:R}} 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.