Global asymptotics for multiple integrals with boundaries

TitreGlobal asymptotics for multiple integrals with boundaries
Type de publicationArticle de revue
AuteurHowls, C. J , Delabaere, Eric
EditeurDuke University Press
TypeArticle scientifique dans une revue à comité de lecture
Année2002
LangueAnglais
DateJan-04-2002
Numéro2
Pagination199-264
Volume112
Titre de la revueDuke Mathematical Journal
ISSN0012-7094
Résumé en anglais

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.

URL de la noticehttp://okina.univ-angers.fr/publications/ua8541
DOI10.1215/S0012-9074-02-11221-6
Titre abrégéDuke Math. J.