99-410 Johannes Sj strand

Complete asymptotics for correlations of Laplace integrals in the semi-classical limit. (233K, Plain TeX) Oct 29, 99

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Abstract. In this paper we study the exponential asymptotics of correlations at large distance associated to a measure of Laplace type. As in [S1], [BJS], we look at a semi-classical limit. While in those papers we got the exponential decay rates and the prefactor only up to some factor $(1+{\cal O}(h^{1/2}))$, where $h$ denotes the small semi-classical parameter, we now get full asymptotic expansions. The main strategy is the same as in the quoted papers, namely to use an identity ([HS]) involving the Witten Laplacian of degree 1, and a Grushin (Feshbach) reduction for the bottom of the spectrum of this operator. The essential difference is however that we now have to use higher order Grushin problems (amounting to the study of a larger part of the bottom of th spectrum). In a perturbative case, the strategy of higher order Grushin problems was recently implemented by W.M.Wang [W] to get a few terms in the perturbative expansion of the decay rate.

Files: 99-410.src( 99-410.keywords , Highordcorr.tex )