A lower bound for Garsia's entropy for certain Bernoulli convolutions

Kevin G. Hare, Nikita Sidorov

Let $\beta \in (1,2)$ be a Pisot number and let $H_{\beta }$ denote Garsia's entropy for the Bernoulli convolution associated with $\beta$. Garsia, in 1963 showed that $H_{\beta }<1$ for any Pisot $\beta$. Fo…