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Pré-Publication, Document De Travail Année : 2013

Random differences in Szemerédi's theorem and related results

Résumé

We introduce a new, elementary method for studying random differences in arithmetic progressions and convergence phenomena along random sequences of integers. We apply our method to obtain significant improvements on two results. The first one concerns existence of arithmetic progresseions of given length in any set of integers of positive density, with differences in a random subset of the integers. The second one concerns almost everywhere convergence of double ergodic averages along partially random sequences.
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Dates et versions

hal-00842122 , version 1 (07-07-2013)
hal-00842122 , version 2 (06-05-2014)

Identifiants

  • HAL Id : hal-00842122 , version 2

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Nikos Frantzikinakis, Emmanuel Lesigne, Mate Wierdl. Random differences in Szemerédi's theorem and related results. 2013. ⟨hal-00842122v2⟩
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