Parking functions are a novel combinatorial object that come
up in computer science hashing, in chip-firing games, MacDonald
polynomials and ‘all over the place’. One way to study a new object is
to ask ‘what does a typical one ‘look like’?’. In joint work with
Angela Hicks, we find new facts about parking functions (what’s the
distribution of pi(1)?) and new uses for for some esoteric facts about
Brownian excursion. The search also illuminates the statistical
mechanics mantra of equivalence of ensembles.