2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168191We consider an i.i.d. random environment with a strong form of transience on the two dimensional integer lattice. Namely, the walk always moves forward in the y-direction. We prove a functional CLT for the quenched expected position of the random walk indexed by its level crossing times. We begin with a variation of the Martingale Central Limit Theorem. The main part of the paper checks the conditions of the theorem for our problem.21 pages, 2 figuresProbability60K37,60F05,60F17,82D30text