Self-intersections in combinatorial topology: statistical structure

DOI10.1007/s00222-011-0350-7zbMath1252.57002arXiv1012.0580OpenAlexW2042920539MaRDI QIDQ421024

Steven P. Lalley, Moira Chas

Publication date: 23 May 2012

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.0580

zbMATH Keywords

closed orientable surfacerandom words in generators of fundamental group

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Fundamental group, presentations, free differential calculus (57M05) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (7)

Central limit theorems for counting measures in coarse negative curvature ⋮ Almost simple geodesics on the triply-punctured sphere ⋮ Geometric intersections of loops on surfaces ⋮ Statistical regularities of self-intersection counts for geodesics on negatively curved surfaces ⋮ Experiments Suggesting That the Distribution of the Hyperbolic Length of Closed Geodesics Sampling by Word Length Is Gaussian ⋮ A central limit theorem for random closed geodesics: proof of the Chas-Li-Maskit conjecture ⋮ Estimating the self-intersection number of closed curves on surface by knot method

Cites Work

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• On \(U\)-statistics and von Mises statistics for a special class of Markov chains
• Combinatorial Lie bialgebras of curves on surfaces.
• Growth of the number of simple closed geodesics on hyperbolic surfaces
• Self-Intersection Numbers of Curves in the Doubly Punctured Plane
• Self-Intersection Numbers of Curves on the Punctured Torus
• On U-statistics and v. mise? statistics for weakly dependent processes
• A Class of Statistics with Asymptotically Normal Distribution

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