  We study the large $N$ 't Hooft expansion of the partition function of 2d
$U(N)$ Yang-Mills theory on a torus. We compute the $1/N$ genus expansion of
both the chiral and the full partition function of 2d Yang-Mills using the
recursion relation found by Kaneko and Zagier with a slight modification. Then
we study the large order behavior of this genus expansion, from which we
extract the non-perturbative correction using the resurgence relation. It turns
out that the genus expansion is not Borel summable and the coefficient of
1-instanton correction, the so-called Stokes parameter, is pure imaginary. We
find that the non-perturbative correction obtained from the resurgence is
reproduced from a certain analytic continuation of the grand partition function
of a system of non-relativistic fermions on a circle. Our analytic continuation
is different from that considered in hep-th/0504221.
