AbstractIn nearest neighbor random walk on ann‐dimensional cube a particle moves to one of its nearest neighbors (or stays fixed) with equal probability. the particle starts at 0. How long does it take to reach its stationary distribution? in fact, this occurs surprisingly rapidly. Previous analysis has shown that the total variation distance to stationarity is large if the number of stepsNis1/4nlogn. This paper derives an explicit expression for the variation distance asn→ ∞ in the transition regionN˜ 1/4nlogn. This permits the first careful evaluation of a cutoff phenomenon observed in a wide variety of Markov chains. the argument involves Fourier analysis to express the probability as a contour integral and saddle point approximation. the asymptotic results are in good agreement with numerical results fornas small