  We study uniform and non-uniform model sets in arbitrary locally compact
second countable (lcsc) groups, which provide a natural generalization of
uniform model sets in locally compact abelian groups as defined by Meyer and
used as mathematical models of quasi-crystals. We then define a notion of
auto-correlation for subsets of finite local complexitiy in arbitrary lcsc
groups, which generalizes Hof's classical definition beyond the class of
amenable groups, and provide a formula for the auto-correlation of a regular
model set. Along the way we show that the punctured hull of an arbitrary
regular model set admits a unique invariant probability measure, even in the
case where the punctured hull is non-compact and the group is non-amenable. In
fact this measure is also the unique stationary measure with respect to any
admissible probability measure.
