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Global asymptotics for multiple integrals with boundaries

Global asymptotics for multiple integrals with boundaries
Global asymptotics for multiple integrals with boundaries
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.
0012-7094
199-264
Delabaere, E.
03408358-5b62-4a0f-8e7b-299e9de4e823
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560
Delabaere, E.
03408358-5b62-4a0f-8e7b-299e9de4e823
Howls, C.J.
66d3f0f0-376c-4f7a-a206-093935e6c560

Delabaere, E. and Howls, C.J. (2002) Global asymptotics for multiple integrals with boundaries. Duke Mathematical Journal, 112 (2), 199-264. (doi:10.1215/S0012-9074-02-11221-6).

Record type: Article

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.

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More information

Published date: 2002

Identifiers

Local EPrints ID: 29213
URI: http://eprints.soton.ac.uk/id/eprint/29213
ISSN: 0012-7094
PURE UUID: fc2b9d63-70a1-414e-a779-497ee190b550
ORCID for C.J. Howls: ORCID iD orcid.org/0000-0001-7989-7807

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Date deposited: 12 May 2006
Last modified: 17 Dec 2019 01:53

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