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 -