Abstract
This paper derives the asymptotic expansions of a wide class of Gaussian function space integrals under the assumption that the minimum points of the action form a nondegenerate manifold. Such integrals play an important role in recent physics. This paper also proves limit theorems for related probability measures, analogous to the classical law of large numbers and central limit theorem.
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Communicated by B. Simon
Alfred P. Sloan Research Fellow. Research supported in part by NSF Grant MCS-80-02149
Research supported in part by NSF Grant MCS-80-02140
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Ellis, R.S., Rosen, J.S. Asymptotic analysis of Gaussian integrals, II: Manifold of minimum points. Commun.Math. Phys. 82, 153–181 (1981). https://doi.org/10.1007/BF02099914
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DOI: https://doi.org/10.1007/BF02099914