Cited by 1,472Black Holes and Theoretical PhysicsAlgebraic Geometry and Number TheoryRandom Matrices and Applications

Intersection theory on the moduli space of curves and the matrix airy function

Kontsevich, Maxim·1992·Communications in Mathematical Physics

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Crossref · 10.1007/bf02099526

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22 of 22 references verified0 citation errors · 0 not checkable

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  • The Airy density of eigenvalues is given by equation (4.10).

    “where the Airy density of eigenvalues is given by [58,59]”

    From Free energy from replica wormholes (2021) · cites this paper as [59]

  • A simple recursion formula to compute integrals over psi-classes and Weil-Petersson form was conjectured by Witten and proven by Kontsevich.

    “A simple recursion formula to compute this type of integrals over psi-classes and Weil–Petersson form (or more generally kappa-classes) was conjectured by Witten (1991b) and proven by Kontsevich (1992).”
  • The connection between JT gravity and random matrix models can be seen in the intersection number approach to computing Weil-Petersson volumes, since those can be obtained in a double-scaled matrix model through the Witten-Kontsevich theorem.

    “This connection can be seen in the intersection number approach to computing Weil–Petersson volumes (4.19), since those can be obtained in a double-scaled matrix model through the Witten–Kontsevich theorem (Witten 1991b; Kontsevich 1992).”

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Authors
Kontsevich, M.
Affiliations
Max Planck Institute for Mathematics (DE)
Corresponding author
Kontsevich, Maxim
Venue
Communications in Mathematical Physics
Published
1992-06
Volume
147
Issue
1
Pages
1-23
ISSN
  • 0010-3616 (ISSN-L)
  • 1432-0916
OpenAlex
W1972563066
Cited by
1,472
References
22
Citations by year
2026: 17 · 2025: 60 · 2024: 53 · 2023: 57 · 2022: 53 · 2021: 108 · 2020: 70 · 2019: 42 · 2018: 57 · 2017: 55 · 2016: 50 · 2015: 56 · 2014: 44 · 2013: 42 · 2012: 37
FWCI
23.98
Type
journal article
Language
en
Open access
closed
Locations
  • Communications in Mathematical Physics (publishedVersion)
  • Project Euclid (Cornell University) (submittedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Mathematics › Geometry and Topology › Algebraic Geometry and Number Theory
  • Physical Sciences › Mathematics › Statistics and Probability › Random Matrices and Applications
Keywords
intersection theory, moduli space of curves, quantum gravity, Korteweg-de Vries equation, matrix models, enumerative geometry

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