Martin Zerner, Stanford University

We consider two models of self-interacting random walks. The first model, called "excited random walk", cf. [1], is a lattice random walks with bias, the strength of which at any given site depends on how often the walker has visited that site before. The consider recurrence/transience and the speed of such walks. The second model, called the "rancher", see [2], is a planar random walk which takes steps of length one but avoids the convex hull of its past positions. We show that this walk has positive lim inf speed.

[1] I. Benjamini, D. Wilson: Excited random walk. ECP 8 (2003) 86-92.

[2] O. Angel, I. Benjamini, B. Virag: Random walks that avoid their past convex hull. ECP 8 (2003) 6-16.