Duke Mathematical Journal

Global asymptotics for multiple integrals with boundaries

E. Delabaere and C. J. Howls

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 18 June 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1087575151

Digital Object Identifier
doi:10.1215/S0012-9074-02-11221-6

Mathematical Reviews number (MathSciNet)
MR1894360

Zentralblatt MATH identifier
1060.30049

Subjects
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]

Citation

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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