Duke Mathematical Journal

Global asymptotics for multiple integrals with boundaries

E. Delabaere and C. J. Howls

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Under convenient geometric assumptions, the saddle-point method for multidimensional Laplace integrals is extended to the case where the contours of integration have boundaries. The asymptotics are studied in the case of nondegenerate and of degenerate isolated critical points. The incidence of the Stokes phenomenon is related to the monodromy of the homology via generalized Picard-Lefschetz formulae and is quantified in terms of geometric indices of intersection. Exact remainder terms and the hyperasymptotics are then derived. A direct consequence is a numerical algorithm to determine the Stokes constants and indices of intersections. Examples are provided.

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Duke Math. J., Volume 112, Number 2 (2002), 199-264.

First available in Project Euclid: 18 June 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32C30: Integration on analytic sets and spaces, currents {For local theory, see 32A25 or 32A27}
Secondary: 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]


Delabaere, E.; Howls, C. J. Global asymptotics for multiple integrals with boundaries. Duke Math. J. 112 (2002), no. 2, 199--264. doi:10.1215/S0012-9074-02-11221-6. https://projecteuclid.org/euclid.dmj/1087575151

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