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Perturbation theory fails to describe the low-energy phenomenology of QCD, like confinement, the mass gap, and the masses of hadrons. Invoking the Wilson’s operator expansion, one can extend perturbative expansions to trans-series, which contain some non-perturbative information encoded in the vacuum condensates. Motivated by this, we will discuss the Gross--Neveu model, a toy QFT of N fermions in 1+1 dimensions which shares some of the non-perturbative properties of QCD. This toy model is amenable to some exact results when the number of fermions N is large. In particular, the two-point function of the fermions can be computed exactly at the first non-trivial order in 1/N. We then compare this result with a direct computation of the first coefficients of the Wilson’s operator expansion, also at large N, and find a perfect match. This provides a precise test for the validity of the operator expansion and the methods used to compute its coefficients.