Resurgence and holonomy of the $\phi^{2k}$ model in zero dimension

Abstract

We describe the resurgence properties of some partition functions corresponding to field theories in dimension 0. We show that these functions satisfy linear differential equations with polynomial coefficients and then use elementary stability results or holonomic functions to prove resurgence properties, enhancing previously known results on growth estimates for the formal series involved, which had been obtained through a delicate combinatorics.