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Random Dirichlet series arising from records

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We study the distributions of the random Dirichlet series with parameters (s, b) defined by S=¥sum_{n=1}¥frac{I_n}{ns}, where (I_n) is an independent sequence of Bernoulli random variables taking value 1 with probability 1/n^b and 0 otherwise. The random series of this type is motivated by the record indicator sequence(and also by random walks on groups). By estimates of exponential sums by van der Corput, we specify the parameter region where the distributions have densities. Joint work with Yuval Peres (Microsoft Research) and Ron Peled (Tel Aviv).

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