Global asymptotics for multiple integrals with boundaries

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.

Type de document :
Article dans une revue
Duke Mathematical Journal, Duke University Press, 2002, 112 (2), pp.199-264. 〈10.1215/S0012-9074-02-11221-6〉
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Contributeur : Okina Université d'Angers <>
Soumis le : mardi 2 octobre 2018 - 20:33:12
Dernière modification le : mardi 30 octobre 2018 - 14:06:06

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C. Howls, Eric Delabaere. Global asymptotics for multiple integrals with boundaries. Duke Mathematical Journal, Duke University Press, 2002, 112 (2), pp.199-264. 〈10.1215/S0012-9074-02-11221-6〉. 〈hal-01886527〉

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