Complexity of random smooth functions on compact manifolds

2012/01/24 by Nicolaescu, Liviu I.
#15B52 #42C10 #53C65 #58K05 #60D05 #60G15 #60G60 #Differential Geometry (math.DG) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1201.4972

Abstract

We relate the distribution of eigenvalues of a random symmetric matrix in the Gaussian Orthogonal Ensemble to the distribution of critical values of a random linear combination of eigenfunctions of the Laplacian on a compact Riemann manifold. We then prove a central limit theorem describing what happens when the dimension of the manifold is very large.

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