2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102278We 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 FieldsProbabilitytext