Maximal Arithmetic Progressions in Random Subsets

  title={Maximal Arithmetic Progressions in Random Subsets},
  author={Itai Benjamini and Ariel Yadin and Ofer Zeitouni},
Abstract Let U (N) denote the maximal length of arithmetic progressions in a random uniform subset of {0, 1} . By an application of the Chen-Stein method, we show that U (N) − 2 log N/ log 2 converges in law to an extreme type (asymmetric) distribution. The same result holds for the maximal length W (N) of arithmetic progressions (mod N). When considered in the natural way on a common probability space, we observe that U / log N converges almost surely to 2/ log 2, while W / log N does not… CONTINUE READING

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