  We consider uniform random permutations drawn from a family enumerated
through generating trees. We develop a new general technique to establish a
central limit theorem for the number of consecutive occurrences of a fixed
pattern in such permutations.
  We propose a technique to sample uniform permutations in such families as
conditioned random colored walks. Building on that, we derive the behavior of
the consecutive patterns in random permutations studying properties of the
consecutive increments in the corresponding random walks. The method applies to
families of permutations with a one-dimensional-labeled generating tree
(together with some technical assumptions) and implies local convergence for
random permutations in such families. We exhibit ten different families of
permutations, most of them being permutation classes, that satisfy our
assumptions.
  To the best of our knowledge, this is the first work where generating trees -
which were introduced to enumerate combinatorial objects - have been used to
establish probabilistic results.
