Typical representatives of free homotopy classes in multi-punctured plane

Maxim Arnold, Yuliy Baryshnikov, Yuriy Mileyko

研究成果: Contribution to journalArticle査読

抄録

We show that a uniform probability measure supported on a specific set of piecewise linear loops in a nontrivial free homotopy class in a multi-punctured plane is overwhelmingly concentrated around loops of minimal lengths. Our approach is based on extending Mogulskii's theorem to closed paths, which is a useful result of independent interest. In addition, we show that the above measure can be sampled using standard Markov Chain Monte Carlo techniques, thus providing a simple method for approximating shortest loops.

本文言語英語
ページ(範囲)623-659
ページ数37
ジャーナルJournal of Topology and Analysis
11
3
DOI
出版ステータス出版済み - 9 1 2019

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology

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