We study the high dimensional asymptotics of the expected number of critical points of a given Morse index of Gaussian random holomorphic sections over complex projective space. We explicitly compute the exponential growth rate of the expected number of critical points of the largest index and of diverging indices at various rates as well as the exponential growth rate for the expected number of critical points (regardless of index). We also compute the distribution of the critical values for the expected number of critical points of smallest index.
Correlations between zeros and critical points of random analytic functions
On critical points of Gaussian random fields under diffeomorphic transformations
A stationary process associated with the Dirichlet distribution arising from the complex projective space
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