Corpus ID: 10620992

Random Morse functions and spectral geometry

@article{Nicolaescu2012RandomMF,
  title={Random Morse functions and spectral geometry},
  author={L. Nicolaescu},
  journal={arXiv: Differential Geometry},
  year={2012}
}

L. Nicolaescu

Published 2012

Mathematics

arXiv: Differential Geometry

We study random Morse functions on a Riemann manifold $(M^m,g)$ defined as a random Gaussian weighted superpositions of eigenfunctions of the Laplacian of the metric $g$. The randomness is determined by a fixed Schwartz function $w$ and a small parameter $\varepsilon>0$. We first prove that as $\varepsilon\to 0$ the expected distribution of critical values of this random function approaches a universal measure on $\mathbb{R}$, independent of $g$, that can be explicitly described in terms the… CONTINUE READING

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