Poisson approximation of the length spectrum of random surfaces

Bram Petri; Christoph Thaele

Poisson approximation of the length spectrum of random surfaces

Probability 2017-11-28 v2 Differential Geometry Geometric Topology

Authors: Bram Petri , Christoph Thaele

Abstract

Multivariate Poisson approximation of the length spectrum of random surfaces is studied by means of the Chen-Stein method. This approach delivers simple and explicit error bounds in Poisson limit theorems. They are used to prove that Poisson approximation applies to curves of length up to order $o(\log\log g)$ with $g$ being the genus of the surface.

Keywords

Poisson approximation length spectrum random surfaces Chen-Stein method error bounds Poisson limit theorems genus of surface

Cite

@article{arxiv.1605.00415,
  title  = {Poisson approximation of the length spectrum of random surfaces},
  author = {Bram Petri and Christoph Thaele},
  journal= {arXiv preprint arXiv:1605.00415},
  year   = {2017}
}

Comments

22 pages, 2 figures. To appear in Indiana Univ. Math. J

Poisson approximation of the length spectrum of random surfaces

Abstract

Keywords

Cite

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