Complexity of random smooth functions on compact manifolds
Differential Geometry
2014-03-18 v4 Probability
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.
Cite
@article{arxiv.1201.4972,
title = {Complexity of random smooth functions on compact manifolds},
author = {Liviu I. Nicolaescu},
journal= {arXiv preprint arXiv:1201.4972},
year = {2014}
}
Comments
23 pages, LaTex, to appear Indiana U. Math. J