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A concentration function estimate and intersective sets from matrices

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Abstract

We give several sufficient conditions on an infinite integer matrix (d ij ) for the set R = {Σ ij∈α, i>j d ij : α ⊂ ℕ, |α| < ∞} to be a density intersective set, including the cases d nj = j n(1 + O(1/n 1+ε)) and \(0 < d_{nj} = o(\sqrt {n/\log n} )\). For the latter, a concentration function estimate that is of independent interest is applied to sums of sequences of 2-valued random variables whose means may grow as \(\sqrt {n/\log n} \).

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, 38111, USA

    Paul Balister & Randall McCutcheon

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  1. Paul Balister
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  2. Randall McCutcheon
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Correspondence to Paul Balister.

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Balister, P., McCutcheon, R. A concentration function estimate and intersective sets from matrices. Isr. J. Math. 189, 413–436 (2012). https://doi.org/10.1007/s11856-011-0176-4

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  • DOI: https://doi.org/10.1007/s11856-011-0176-4

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