  We study the number of occurrences of any fixed vincular permutation pattern.
We show that this statistics on uniform random permutations is asymptotically
normal and describe the speed of convergence. To prove this central limit
theorem, we use the method of dependency graphs. The main difficulty is then to
estimate the variance of our statistics. We need a lower bound on the variance,
for which we introduce a recursive technique based on the law of total
variance.
