Largest projections for random walks and shortest curves in random mapping tori

Alessandro Sisto, Samuel J. Taylor

Research output: Contribution to journalArticle

Abstract

We show that the largest subsurface projection distance between a marking and its image under the nth step of a random walk grows logarithmically in n, with probability approaching 1 as n → ∞. Our setup is general and also applies to (relatively) hyperbolic groups and to Out(Fn). We then use this result to prove Rivin’s conjecture that for a random walk (wn) on the mapping class group, the shortest geodesic in the hyperbolic mapping torus Mwn has length on the order of 1/log2(n).

Original languageEnglish
Pages (from-to)293-321
Number of pages29
JournalMathematical Research Letters
Volume26
Issue number1
Early online date7 Jun 2019
DOIs
Publication statusPublished - 2019

ASJC Scopus subject areas

  • Mathematics(all)

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