On the number of equilibria with a given number of unstable directions
classification
🧮 math.PR
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numberequilibriadirectionsunstableasymptoticsaveragecomputediscuss
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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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