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• W2201062049 abstract "We prove a Chern-Lashof type formula computing the expected number of critical points of smooth function on a smooth manifold $M$ randomly chosen from a finite dimensional subspace $Vsubset C^infty(M)$ equipped with a Gaussian probability measure. We then use this formula this formula to find the asymptotics of the expected number of critical points of a random linear combination of a large number eigenfunctions of the Laplacian on the round sphere, tori, or a products of two round spheres. In the case $M=S^1$ we show that the number of critical points of a trigonometric polynomial of degree $leq nu$ is a random variable $Z_nu$ with expectation $E(Z_nu)sim 2sqrt{0.6},nu$ and variance $var(Z_nu)sim cnu$ as $nuto infty$, $capprox 0.35$." @default.
• W2201062049 created "2016-06-24" @default.
• W2201062049 creator A5063741270 @default.
• W2201062049 date "2010-08-30" @default.
• W2201062049 modified "2023-10-01" @default.
• W2201062049 title "Critical sets of random smooth functions on products of spheres" @default.
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