  We study the strong spatial mixing (decay of correlation) property of proper
$q$-colorings of random graph $G(n, d/n)$ with a fixed $d$. The strong spatial
mixing of coloring and related models have been extensively studied on graphs
with bounded maximum degree. However, for typical classes of graphs with
bounded average degree, such as $G(n, d/n)$, an easy counterexample shows that
colorings do not exhibit strong spatial mixing with high probability.
Nevertheless, we show that for $q\ge\alpha d+\beta$ with $\alpha>2$ and
sufficiently large $\beta=O(1)$, with high probability proper $q$-colorings of
random graph $G(n, d/n)$ exhibit strong spatial mixing with respect to an
arbitrarily fixed vertex. This is the first strong spatial mixing result for
colorings of graphs with unbounded maximum degree. Our analysis of strong
spatial mixing establishes a block-wise correlation decay instead of the
standard point-wise decay, which may be of interest by itself, especially for
graphs with unbounded degree.
