  The topic of this paper is the distributed and incremental generation of long
executions of concurrent systems, uniformly or more generally with weights
associated to elementary actions. Synchronizing sequences of letters on
alphabets sharing letters are known to produce a trace in the concurrency
theoretic sense, i.e., a labeled partially ordered set. We study the
probabilistic aspects by considering the synchronization of Bernoulli sequences
of letters, under the light of Bernoulli and uniform measures recently
introduced for trace monoids. We introduce two algorithms that produce random
traces, using only local random primitives. We thoroughly study some specific
examples, the path model and the ring model, both of arbitrary size. For these
models, we show how to generate any Bernoulli distributed random traces, which
includes the case of uniform generation.
