Abstract
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 \(\sqrt{\log t}\).
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Amir, G., Benjamini, I. & Kozma, G. Excited random walk against a wall. Probab. Theory Relat. Fields 140, 83–102 (2008). https://doi.org/10.1007/s00440-007-0058-1
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DOI: https://doi.org/10.1007/s00440-007-0058-1