 99410 Johannes Sj strand
 Complete asymptotics for correlations of Laplace integrals in the
semiclassical 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 semiclassical 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 semiclassical 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.
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