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

2017/09/12 by Xavier Garcia, Garcia, Xavier · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1709.04021

openalex publication_date 2017/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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