Another algebraic variational principle for the spectral curve of matrix models

B. Eynard

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arXiv · 1407.8324

Another algebraic variational principle for the spectral curve of matrix models

B. Eynard

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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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B. Eynard. 2014-07-31. Another algebraic variational principle for the spectral curve of matrix models. https://arxiv.org/abs/1407.8324

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