Low-energy spectrum of Toeplitz operators with a miniwell

In the semiclassical limit, it is well-known that the first eigenvector of a Toeplitz operator concentrates on the minimal set of the symbol. In this paper, we give a more precise criterion for concentration in the case where the minimal set of the symbol is a submanifold, in the spirit of the “miniwell condition” of Helffer-Sj{"o}strand.