Maxima of partial sums indexed by geometrical structures

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The maxima of partial sums indexed by squares and rectangles over lattice points and random cubes are studied in this paper. For some of these problems, the dimension (d = 1, d = 2 and d ≥ 3) significantly affects the limit behavior of the maxima. However, for other problems, the maxima behave almost the same as their one-dimensional counterparts. The tools for proving these results are large deviations, the Chen-Stein method, number theory and inequalities of empirical processes.

Original languageEnglish (US)
Pages (from-to)1854-1892
Number of pages39
JournalAnnals of Probability
Issue number4
StatePublished - Oct 2002


  • Chen-Stein method
  • Inequalities of empirical processes
  • Large deviations
  • Maxima
  • Number theory

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