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arXiv · 1709.04021

On the number of equilibria with a given number of unstable directions

Xavier Garcia
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Abstract

We compute the large-dimensional asymptotics for the average number of equilibria with a fixed number of unstable directions for random Gaussian ODEs on a sphere. We also discuss the effects that the value of the Lagrange multiplier of the vector field has on the number of such equilibria. This was a problem posed by Fyodorov.

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Xavier Garcia. 2017-09-12. On the number of equilibria with a given number of unstable directions. https://arxiv.org/abs/1709.04021

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