  We establish the first known upper bound on the exact and Wyner's common
information of $n$ continuous random variables in terms of the dual total
correlation between them (which is a generalization of mutual information). In
particular, we show that when the pdf of the random variables is log-concave,
there is a constant gap of $n^{2}\log e+9n\log n$ between this upper bound and
the dual total correlation lower bound that does not depend on the
distribution. The upper bound is obtained using a computationally efficient
dyadic decomposition scheme for constructing a discrete common randomness
variable $W$ from which the $n$ random variables can be simulated in a
distributed manner. We then bound the entropy of $W$ using a new measure, which
we refer to as the erosion entropy.
