# Another algebraic variational principle for the spectral curve of matrix models

Abstract : We propose an alternative variational principle whose critical point is the algebraic plane curve associated to a matrix model (the spectral curve, i.e. the large $N$ limit of the resolvent). More generally, we consider a variational principle that is equivalent to the problem of finding a plane curve with given asymptotics and given cycle integrals. This variational principle is not given by extremization of the energy, but by the extremization of an "entropy".
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Cited literature [15 references]

https://hal-cea.archives-ouvertes.fr/cea-01277989
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Submitted on : Tuesday, February 23, 2016 - 2:51:50 PM
Last modification on : Tuesday, October 6, 2020 - 9:48:13 AM
Long-term archiving on: : Tuesday, May 24, 2016 - 2:00:11 PM

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1407.8324v1.pdf
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• HAL Id : cea-01277989, version 1
• ARXIV : 1407.8324

### Citation

Bertrand Eynard. Another algebraic variational principle for the spectral curve of matrix models. 2016. ⟨cea-01277989⟩

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