On the Gibbs properties of Bernoulli convolutions related to   $\beta$-numeration in multinacci bases
  We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the $\beta$-numeration. A matrix decomposition of these measures is obtained in the case when $\beta$ is a PV number. We also determine their Gibbs properties for $\beta$ being a multinacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible. 
Eric Olivier, Nikita Sidorov, Alain Thomas