KdV integrability in GUE correlators
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910073888964608 |
|---|---|
| author | Yang, Di |
| author_facet | Yang, Di |
| contents | Okounkov [36] proved a remarkable formula relating $n$-point GUE (Gaussian unitary ensemble) correlators of a fixed genus to Witten's intersection numbers of the same genus. The partition function of GUE correlators is a tau-function for the Toda lattice hierarchy. In this note, based on the knowledge of these two statements we give a new proof of the Witten--Kontsevich theorem, that relates Witten's intersection numbers to the KdV (Korteweg--de Vries) integrable hierarchy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24956 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | KdV integrability in GUE correlators Yang, Di Mathematical Physics Algebraic Geometry Exactly Solvable and Integrable Systems Okounkov [36] proved a remarkable formula relating $n$-point GUE (Gaussian unitary ensemble) correlators of a fixed genus to Witten's intersection numbers of the same genus. The partition function of GUE correlators is a tau-function for the Toda lattice hierarchy. In this note, based on the knowledge of these two statements we give a new proof of the Witten--Kontsevich theorem, that relates Witten's intersection numbers to the KdV (Korteweg--de Vries) integrable hierarchy. |
| title | KdV integrability in GUE correlators |
| topic | Mathematical Physics Algebraic Geometry Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2603.24956 |