Discrete Bernoulli convolutions: An algorithmic approach toward bound improvement

Abstract

Abstract. In this paper we consider a discrete version of the Bernoulli convolution problem traditionally studied via functional analysis. We develop an algorithm which bounds the Bernoulli sequences, and we give a significant improvement on the best known bound.

Bernoulli convolutions and 1D dynamics

“…For the moment however, our results on piecewise convexity are restricted to some special values of λ, although we are able to run numerical approximations for any λ. There have been previous numerical investigations into Bernoulli convolutions, we mention in particular the work of Benjamini and Solomyak [1] and of Calkin et al [2,3].…”