TY - JOUR

T1 - Multifractal structure of Bernoulli convolutions

AU - Jordan, Thomas

AU - Shmerkin, Pablo

AU - Solomyak, Boris

PY - 2011

Y1 - 2011

N2 - Let vλp 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, δλ,p (a) is nonempty and, moreover, has positive Hausdorff dimension, for many values of a. This happens even in parameter regions for which vλp is typically absolutely continuous.

AB - Let vλp 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, δλ,p (a) is nonempty and, moreover, has positive Hausdorff dimension, for many values of a. This happens even in parameter regions for which vλp is typically absolutely continuous.

UR - http://www.scopus.com/inward/record.url?scp=85018192948&partnerID=8YFLogxK

U2 - 10.1017/S0305004111000466

DO - 10.1017/S0305004111000466

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AN - SCOPUS:85018192948

SN - 0305-0041

VL - 151

SP - 521

EP - 539

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 3

ER -