We consider finite Bernoulli convolutions with a parameter 1/2<r<1
supported on a discrete point set, generically of size 2N. These sequences
are uniformly distributed with respect to the infinite Bernoulli convolution
measure νr, as N tends to infinity. Numerical evidence suggests that for
a generic r, the distribution of spacings between appropriately rescaled
points is Poissonian. We obtain some partial results in this direction; for
instance, we show that, on average, the pair correlations do not exhibit
attraction or repulsion in the limit. On the other hand, for certain algebraic
r the behavior is totally different.Comment: 17 pages, 6 figure