Complexity of random smooth functions on compact manifolds. I

Details Complexity of random smooth functions on compact manifolds. I Complexity of random smooth functions on compact manifolds. I

2012-01-24

arxiv.org/abs/1201.4972v2

Mathematics

Differential Geometry

20 pages, LaTex

Scientific paper

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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