Resumen de How short might be the longest run in a dynamical coin tossing sequence

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• Let X1;X2; : : : denote i.i.d. random bits each taking the values 1 and 0 with respective probabilities 1=2 and 1=2. A well-known theorem of Erd}os and R¶enyi [2] describes the limit distribution of the length of the longest contiguous run of ones in X1;X2; : : : ;Xn as n ! 1. Benjamini et al. ([1] Theorem 1.4) demonstrated the existence of unusual times, provided that the bits undergo equilibrium dynamics in time. In fact they prove that the dynamics produces much longer runs than the original model. In the present paper we study the length of the shortest run in the presence of the dynamics.