  We study quantum JT gravity at finite cutoff using a mapping to the
statistical mechanics of a self-avoiding loop in hyperbolic space, with
positive pressure and fixed length. The semiclassical limit (small $G_N$)
corresponds to large pressure, and we solve the problem in that limit in three
overlapping regimes that apply for different loop sizes. For intermediate loop
sizes, a semiclassical effective description is valid, but for very large or
very small loops, fluctuations dominate. For large loops, this quantum regime
is controlled by the Schwarzian theory. For small loops, the effective
description fails altogether, but the problem is controlled using a conjecture
from the theory of self-avoiding walks.
