Abstract
In this article, we want to present a stationary phase theorem appearing in a recent article by J. Sjöstrand ( Ann. Inst. H. Poincaré Phys. Théor., in press) and explain the role it can play in the context of statistical mechanics. This theorem is also technically connected to the semi-classical determination of eigenvalues for a Schrödinger operator in large dimension and also, in the same spirit, with small or large temperature expansions.
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