On a class of random walks in simplexes

Tuan Minh Nguyen, Stanislav Volkov

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3 Citations (Scopus)


We study the limit behaviour of a class of random walk models taking values in the standard d-dimensional simplex. From an interior point z, the process chooses one of the vertices of the simplex, with probabilities depending on z, and then the particle randomly jumps to a new location z′ on the segment connecting z to the chosen vertex. In some special cases, using properties of the Beta distribution, we prove that the limiting distributions of the Markov chain are Dirichlet. We also consider a related history-dependent random walk model in [0, 1] based on an urn-type scheme. We show that this random walk converges in distribution to an arcsine random variable.

Original languageEnglish
Pages (from-to)409-428
Number of pages20
JournalJournal of Applied Probability
Issue number2
Publication statusPublished - 16 Jul 2020


  • Dirichlet distribution
  • iterated random functions
  • Keywords: Random walks in simplexes
  • stick-breaking process

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