We develop an exact determinantal formula for the probability that the Airy2
process is bounded by a function g on a finite interval. As an application, we provide
a direct proof that sup(A2(x) − x2) is distributed as a GOE random variable. Both the
continuum formula and the GOE result have applications in the study of the end point of
an unconstrained directed polymer in a disordered environment.We explain Johansson’s
(Commun. Math. Phys. 242(1–2):277–329, 2003) observation that the GOE result follows
from this polymer interpretation and exact results within that field. In a companion
paper (Moreno Flores et al. in Commun. Math. Phys. 2012) these continuum statistics
are used to compute the distribution of the endpoint of directed polymers.