  In this paper we prove that a uniformly distributed random circular automaton
$\mathcal{A}_n$ of order $n$ synchronizes with high probability (whp). More
precisely, we prove that $$ \mathbb{P}\left[\mathcal{A}_n \text{
synchronizes}\right] = 1- O\left(\frac{1}{n}\right). $$ The main idea of the
proof is to translate the synchronization problem into properties of a random
matrix; these properties are then handled with tools of the probabilistic
method. Additionally, we provide an upper bound for the probability of
synchronization of circular automata in terms of chromatic polynomials of
circulant graphs.
