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1 April 2002 Global asymptotics for multiple integrals with boundaries
E. Delabaere, C. J. Howls
Duke Math. J. 112(2): 199-264 (1 April 2002). DOI: 10.1215/S0012-9074-02-11221-6

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.

Citation

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E. Delabaere. C. J. Howls. "Global asymptotics for multiple integrals with boundaries." Duke Math. J. 112 (2) 199 - 264, 1 April 2002. https://doi.org/10.1215/S0012-9074-02-11221-6

Information

Published: 1 April 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1060.30049
MathSciNet: MR1894360
Digital Object Identifier: 10.1215/S0012-9074-02-11221-6

Subjects:
Primary: 32C30
Secondary: 41A60

Rights: Copyright © 2002 Duke University Press

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Vol.112 • No. 2 • 1 April 2002
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