A concentration function estimate and intersective sets from matrices


We give several sufficient conditions on an infinite integer matrix (dij) for the set R = {Σij∈α, i>jdij: α ⊂ ℕ, {pipe}α{pipe} < ∞} to be a density intersective set, including the cases dnj = jn(1 + O(1/n1+ε)) and 0 < dnj = o(√n/logn). 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 (√n/logn). © 2011 Hebrew University Magnes Press.

Publication Title

Israel Journal of Mathematics