Intersection theory on the moduli space of curves and the matrix airy function
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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).”
From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as 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).”
From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Kontsevich 1992
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- Authors
- Kontsevich, M.
- Affiliations
- Max Planck Institute for Mathematics (DE)
- Corresponding author
- Kontsevich, Maxim
- ORCID
- 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
- Licence
- www.springer.com/tdm (tdm)
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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