Abstract
AbstractWe discuss a variant, named ‘Rattle’, of the product replacement algorithm. Rattle is a Markov chain, that returns a random element of a black box group. The limiting distribution of the element returned is the uniform distribution. We prove that, if the generating sequence is long enough, the probability distribution of the element returned converges unexpectedly quickly to the uniform distribution.
Publisher
Cambridge University Press (CUP)
Reference19 articles.
1. [8] Kaluba, M. , Kielak, D. and Nowak, P. , On property $(T)$ for $\mathrm{Aut}({\mathbb F}_n)$ and $\mathrm{SL}_n({\mathbb Z})$ . arXiv:1812.03456.
2. Strong bias of group generators: an obstacle to the “product replacement algorithm”
3. The product replacement algorithm and Kazhdan’s property (T);Lubotzky;J.A.M.S.,2001