...The first recurrence time of the initial n-block is the first time the block Xn1 repeats in the sample X ∞ 1 , i.e. Rn = min{k > 0 : Xn0 = Xk+nk } The Wyner-Ziv/Ornstein-Weiss recurrence time theorem =-=[3, 2]-=- states that with probability 1, 1 n logRn → h where h = h((Xn)∞n=1) is the entropy of the process (by convention, all logarithms are in base 2). Our main concern here will be another quantity, the fr...

...The first recurrence time of the initial n-block is the first time the block Xn1 repeats in the sample X ∞ 1 , i.e. Rn = min{k > 0 : Xn0 = Xk+nk } The Wyner-Ziv/Ornstein-Weiss recurrence time theorem =-=[3, 2]-=- states that with probability 1, 1 n logRn → h where h = h((Xn)∞n=1) is the entropy of the process (by convention, all logarithms are in base 2). Our main concern here will be another quantity, the fr...

...PROCESSES 3 which the base point is taken to be one of the corners, do not satisfy the Besicovitch property in higher dimensions; dimension 1 is special in this regard. Most of the complications in =-=[1]-=- came from the attempt to find suitable analogs to this lemma in other groups; there are not many groups that posses such sequences that are also Følner sequences, though some weaker conditions were p...