Multifractal structure of Bernoulli convolutions

Let v_λ^p be the distribution of the random series, where in is a sequence of i.i.d. random variables taking the values 0,1 with probabilities p, 1 - p. These measures are the well-known (biased) Bernoulli convolutions. In this paper we study the multifractal spectrum of vp for typical?. Namely, we investigate the size of the sets Our main results highlight the fact that for almost all, and in some cases all, ? in an appropriate range, δ_λ,p (a) is nonempty and, moreover, has positive Hausdorff dimension, for many values of a. This happens even in parameter regions for which v_λ^p is typically absolutely continuous.