Tracking rates of random walks

Alessandro Sisto*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We show that simple random walks on (non-trivial) relatively hyperbolic groups stay O(log(n))-close to geodesics, where n is the number of steps of the walk. Using similar techniques we show that simple random walks in mapping class groups stay O(nlog(n))-close to geodesics and hierarchy paths. Along the way, we also prove a refinement of the result that mapping class groups have quadratic divergence. An application of our theorem for relatively hyperbolic groups is that random triangles in non-trivial relatively hyperbolic groups are O(log(n))-thin, random points have O(log(n))-small Gromov product and that in many cases the average Dehn function is subasymptotic to the Dehn function.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalIsrael Journal of Mathematics
Issue number1
Early online date5 May 2017
Publication statusPublished - Jun 2017

ASJC Scopus subject areas

  • Mathematics(all)


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