Strict correlation-dimension drop for quartic Salem Bernoulli convolutions

Guozheng Cheng, Xiang Fang, Xueqing Ma +1

For every quartic Salem number $\beta \in (1,2)$, we prove that the Bernoulli convolution ${\nu }_{{\beta }^{-1}}$ with equal weights has correlation dimension strictly less than one. In particular,…