Typical peak sidelobe level of binary sequences

For a binary sequence in given equation, the peak sidelobe level (PSL) is defined as by a certain equation. It is shown that the distribution of M(S_n) is strongly concentrated, and asymptotically almost surely, as per a derived equation. Explicit bounds for the number of sequences outside this range are provided. This improves on the best earlier known bounds due to Moon and Moser [1968] claiming that the typical value in equation 3 and settles to the affirmative a conjecture of Dmitriev and Jedwab [2007] on the growth rate of the typical peak sidelobe.