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    Neunhäuserer, J. 2015. Multifractality of overlapping non-uniform self-similar measures. Monatshefte für Mathematik, Vol. 177, Issue. 3, p. 461.

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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 151, Issue 3
  • November 2011, pp. 521-539

Multifractal structure of Bernoulli convolutions

  • DOI:
  • Published online: 19 August 2011

Let νpλ 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 νpλ for typical λ. Namely, we investigate the size of the sets Our main results highlight the fact that for almost all, and in some cases all, λ in an appropriate range, Δλ, p(α) is nonempty and, moreover, has positive Hausdorff dimension, for many values of α. This happens even in parameter regions for which νpλ is typically absolutely continuous.

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