The peak sidelobe level of random binary sequences

Details The peak sidelobe level of random binary sequences The peak sidelobe level of random binary sequences

2011-05-26

arxiv.org/abs/1105.5178v1

Mathematics

Combinatorics

Scientific paper

Let A_n = (a_0, a_1, ..., a_{n-1}) be taken uniformly from {-1,+1}^n and define M(A_n) := max_{01. It is proved that M(A_n)/\sqrt{n\log n} converges in probability to \sqrt{2}. This settles a problem first studied by Moon and Moser in the 1960s and proves in the affirmative a recent conjecture due to Alon, Litsyn, and Shpunt. It is also shown that the expectation of M(A_n)/\sqrt{n\log n} tends to \sqrt{2}.

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