Small divisors of Bernoulli sums

Let epsilon = {epsilon(i), i >= 1} be a sequence of independent Bernoulli random variables (P{epsilon(i) = 0) = P{epsilon(i) = 1} = 1/2) with basic probability space (Omega, A, P). Consider the sequence of partial sums B-n = epsilon(1) + ... + epsilon(n), n = 1,2,.... We obtain an asymptotic estimate for the probability P{P-(B-n) > zeta} for zeta <= n(c/log log n), c a positive constant.