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

Bertrand Eynard

#### 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".

### Dates and versions

cea-01277989 , version 1 (23-02-2016)

### Identifiers

• HAL Id : cea-01277989 , version 1
• ARXIV :

### Cite

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

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