Journal ArticleDOI
Global asymptotics for multiple integrals with boundaries
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In this article, the saddle-point method for multidimensional Laplace integrals is extended to the case where the contours of integration have boundaries and the asymptotics are studied in the case of nondegenerate and of degenerate isolated critical points.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.read more
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A primer on resurgent transseries and their asymptotics
TL;DR: In this paper, resurgence and transseries are used to encode the complete large-order asymptotic behaviour of the coefficients from a perturbative expansion, generically in terms of (multi) instanton sectors and for each problem in terms with its Stokes constants, which are recast in equivalent physical languages: either a statistical mechanical language, as motions in chains and lattices; or a conformal field theoretical language, with underlying Virasoro-like algebraic structures.
Book
Aspects of Scattering Amplitudes and Moduli Space Localization
TL;DR: In this paper, intersection numbers of certain cohomology classes on the moduli space of genus-zero Riemann surfaces with $n$ punctures, $\mathcal{M}_{0,n}), compute tree-level scattering amplitudes in quantum field theories with a finite spectrum of particles.
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Analytic Combinatorics in Several Variables
Robin Pemantle,Mark C. Wilson +1 more
TL;DR: In this paper, the authors treat the analytic aspects of combinatorial enumeration from a multivariate perspective and present a review of the uses of generating functions in combinatorially enumerative enumeration.
Journal ArticleDOI
A Primer on Resurgent Transseries and Their Asymptotics
TL;DR: In this paper, the authors provide a good introduction to the resurgence and transseries of perturbative expansion models, which can be recast in equivalent physical languages: either a statistical mechanical language, as motions in chains and lattices; or a conformal field theoretical language, with underlying Virasoro-like algebraic structures.
Journal ArticleDOI
Quantum geometry of resurgent perturbative/nonperturbative relations
TL;DR: In this paper, the authors unify these examples in geometric terms, arguing that the all-orders quantum action determines the allorders quantum dual action for quantum spectral problems associated with a classical genus one elliptic curve.
References
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Book
Ordinary differential equations
TL;DR: The fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ODEs was published by as discussed by the authors, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.
Reference BookDOI
Asymptotics and Special Functions
TL;DR: A classic reference, intended for graduate students mathematicians, physicists, and engineers, this book can be used both as the basis for instructional courses and as a reference tool as discussed by the authors, and it can be found in many libraries.