Abstract
Let ε = { ε i , i ≥ 1} be a Rademacher sequence, with partial sums S n = ε 1 +… + ε n , n ≥ 1. Let N k be the k-th even integer such that N k ∥ S N k 2 . We prove that there exists a positive real s, of which the value is explicitly given, such that for any τ > 7 8 , log N k = k s + O(k τ) almost surely.
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