The peak sidelobe level of random binary sequences
Kai‐Uwe Schmidt · Bulletin of the London Mathematical Society · 2014
Let A n = ( a 0 , a 1 , … , a n − 1 ) be drawn uniformly at random from { − 1 , + 1 } n and define M ( A n ) = max 0 1 . It is proved that M ( A n ) / n log n converges in probability to 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 ) / n log n tends to 2 .