  Apollonian gaskets are formed by repeatedly filling the gaps between three
mutually tangent circles with further tangent circles. In this paper we give
explicit formulas for the the limiting pair correlation and the limiting
nearest neighbor spacing of centers of circles from a fixed Apollonian gasket.
These are corollaries of the convergence of moments that we prove. The input
from ergodic theory is an extension of Mohammadi-Oh's Theorem on the
equidisribution of expanding horospheres in infinite volume hyperbolic spaces.
