  Inspired by recent formul\ae\ of Dubrovin, Yang, and Zagier, we interpret the
tau function enumerating stationary Gromov-Witten invariants of $\mathbb{P}^1$
as an isomonodromic tau function associated with a difference equation. As a
byproduct we obtain an analogue of the Kontsevich matrix model for this tau
function. A connection with the Charlier ensemble is also considered.
