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We study a random walk in a N dimensional hypercube and exhibit results aboutstopping times when N diverges. The first theorem discusses the time in whichtwo coupling processes spend to meet. A corollary provides a majorant for thevelocity of convergence to equilibrium. Other three theorems treat,respectively, the time of first return to a point, the time of first return toa fixed set and the time of first arrival in a random set. We prove that thesetimes, under a suitable rescaling, converge in law to a mean one exponentialrandom time.

Aproxima\c{c}\~ao do Equil\'ibrio e Tempos Exponenciais para o Passeio Aleat\'orio no Hipercubo