  The matrix model of ABJM theory can be formulated in terms of a Fermi gas in
an external potential. We show that, in this formalism, vevs of Wilson loops
correspond to averages of operators in the statistical-mechanical problem. This
makes it possible to calculate these vevs at all orders in 1/N, up to
exponentially small corrections, and for arbitrary Chern-Simons coupling, by
using the WKB expansion. We present explicit results for the vevs of 1/6 and
the 1/2 BPS Wilson loops, at any winding number, in terms of Airy functions.
Our expressions are shown to reproduce the low genus results obtained
previously in the 't Hooft expansion.
