A Central Limit Theorem for non-overlapping return times

Abstract

Define the non-overlapping return time of a random process to be the number of blocks that we wait before a particular block reappears. We prove a Central Limit Theorem based on these return times. This result has applications to entropy estimation, and to the problem of determining if digits have come from an independent equidistribted sequence. In the case of an equidistributed sequence, we use an argument based on negative association to prove convergence under weaker conditions.