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Barrera, J., & Ycart, B. (2014). Bounds for left and right window cutoffs. ALEA-Latin Am. J. Probab. Math. Stat., 11(2), 445–458.
Abstract: The location and width of the time window in which a sequence of processes converges to equilibrum are given under conditions of exponential convergence. The location depends on the side: the left-window and right-window cutoffs may have different locations. Bounds on the distance to equilibrium are given for both sides. Examples prove that the bounds are tight.