Geodesic
On a variant of the product replacement algorithm
Glasgow mathematical journal, Tome 66 (2024) no. 1, pp. 221-228

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DOI

We 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.
DOI : 10.1017/S0017089523000435
Mots-clés : Product replacement, Random group elements, Rattle, Markov Processes 
Leedham-Green, C.R. On a variant of the product replacement algorithm. Glasgow mathematical journal, Tome 66 (2024) no. 1, pp. 221-228. doi: 10.1017/S0017089523000435
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