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arXiv · 1201.4972

Complexity of random smooth functions on compact manifolds

Liviu I. Nicolaescu
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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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Liviu I. Nicolaescu. 2014-03-17. Complexity of random smooth functions on compact manifolds. https://arxiv.org/abs/1201.4972

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