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Aleksandrov, Alexander
기하학 수리물리 연구단
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Weighted Hurwitz Numbers and Topological Recursion

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Title
Weighted Hurwitz Numbers and Topological Recursion
Author(s)
Alexander Aleksandrov; G. Chapuy; B. Eynard; J. Harnad
Subject
GROMOV-WITTEN THEORY, ; TAU-FUNCTIONS, ; HYPERGEOMETRIC-FUNCTIONS, ; TODA EQUATIONS, ; MATRIX MODELS, ; MODULI SPACES, ; ENUMERATION, ; CURVES, ; INVARIANTS, ; SYSTEMS
Publication Date
2020-04
Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS, v.375, no.1, pp.237 - 305
Publisher
SPRINGER
Abstract
© 2020, Springer-Verlag GmbH Germany, part of Springer Nature.The KP and 2D Toda τ-functions of hypergeometric type that serve as generating functions for weighted single and double Hurwitz numbers are related to the topological recursion programme. A graphical representation of such weighted Hurwitz numbers is given in terms of weighted constellations. The associated classical and quantum spectral curves are derived, and these are interpreted combinatorially in terms of the graphical model. The pair correlators are given a finite Christoffel–Darboux representation and determinantal expressions are obtained for the multipair correlators. The genus expansion of the multicurrent correlators is shown to provide generating series for weighted Hurwitz numbers of fixed ramification profile lengths. The WKB series for the Baker function is derived and used to deduce the loop equations and the topological recursion relations in the case of polynomial weight functions
URI
https://pr.ibs.re.kr/handle/8788114/8694
DOI
10.1007/s00220-020-03717-0
ISSN
0010-3616
Appears in Collections:
Center for Geometry and Physics(기하학 수리물리 연구단) > 1. Journal Papers (저널논문)
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