关于乘积替换算法的变体

Pub Date : 2024-01-09 DOI:10.1017/s0017089523000435

C.R. Leedham-Green

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引用次数: 0

摘要

我们讨论的是产品替换算法的一个变种，名为 "Rattle"。Rattle 是一个马尔可夫链，它返回一个黑盒子组中的随机元素。返回元素的极限分布是均匀分布。我们证明，如果生成序列足够长，返回元素的概率分布会出乎意料地迅速收敛到均匀分布。

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On a variant of the product replacement algorithm

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.

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