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We study the lower and upper local rates of Poincare recurrence of rotationson the circle by means of symbolic dynamics. As a consequence, we show that ifthe lower rate of Poincare recurrence of an ergodic dynamical system (X,F,mu,T)is greater or equal to 1 mu-almost everywhere, then it is weakly mixing.

Local rates of Poincaré recurrence for rotations and weak mixing