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The genus of a random chord diagram is asymptotically normal

Authors
Journal
Journal of Combinatorial Theory Series A
0097-3165
Publisher
Elsevier
Volume
120
Issue
1
Identifiers
DOI: 10.1016/j.jcta.2012.07.004
Keywords
  • Chord Diagrams
  • Random
  • Genus
  • Limit
  • Distribution
Disciplines
  • Mathematics

Abstract

Abstract Let Gn be the genus of a two-dimensional surface obtained by gluing, uniformly at random, the sides of an n-gon. Recently Linial and Nowik proved, via an enumerational formula due to Harer and Zagier, that the expected value of Gn is asymptotic to (n−logn)/2 for n→∞. We prove a local limit theorem for the distribution of Gn, which implies that Gn is asymptotically Gaussian, with mean (n−logn)/2 and variance (logn)/4.

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