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Some self-interacting random walks with bias

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Speaker: Martin Zerner, Stanford University
Location: 693 Kerr
Start time: Wed, Feb 11 2004, 4:10PM

Abstract: We consider two models of self-interacting random walks: (1) Excited Random Walks: We put two cookies on each integer and start a random walker at 0. Whenever there is at least one cookie at the walker's present location, the walker eats one of these cookies and then jumps to the right with probability p and to the left with probability 1-p, where p is a fixed parameter greater than 1/2. At sites without any cookies left over the walker jumps with probability 1/2 to the right and 1/2 to the left. We consider recurrence, transience and the speed of such walks. Similar models have been investigated e.g. by Benjamini, Wilson, Kozma and Volkov. (2) Rancher: We consider a model due to Angel, Benjamini and Virag, in which a random walker in the plane takes steps of length one but avoids the convex hull of its past positions. We show that this walk has positive lim inf speed.