Excited random walk against a wall
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We analyze random walk in the upper half of a three dimensional lattice which goes down whenever it encounters a new vertex, a.k.a. excited random walk. We show that it is recurrent with an expected number of returns of square-root log n.
16 pages. Revised as per referee remarks. To appear in Probab. Theory Related Fields
16 pages. Revised as per referee remarks. To appear in Probab. Theory Related Fields