Supersymmetric large-order perturbation with the Nicolai map

In rigidly supersymmetric quantum theories, the Nicolai map allows one to turn on a coupling constant (from zero finite value) by keeping (free) functional integration measure but subjecting fields particular nonlocal and nonlinear transformation. A recursive perturbative construction of Nicolai-transformed field configuration expresses it as power series in coupling, with its coefficient function at order $n$ being sum tree diagrams. For quantum-mechanical example, size these diagrams (under certain norm) is estimated $(n{+}1)$st size, their number grows like $n^{-3/2}\times4.967^{\;n}$. Such an asymptotic behavior translates convergence radius for formal expansion map, which establishes non-perturbative existence. The known factorial growth Feynman correlators reproduced combinatorics free-field Wick contractions usual. We expect our results extend higher dimensions, including super Yang-Mills theory.