Cycles in random k-ary maps and the poor performance of random random number generation

Robin Pemantle

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Cycles in random k-ary maps and the poor performance of random random number generation

Robin Pemantle

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Abstract

Knuth shows that iterations of a random function perform poorly on average as a random number generator. He proposes a generalization in which the next value depends on two or more previous values. This note demonstrates, via an analysis of the cycle length of a random k-ary map, the equally poor performance of a random instance in Knuth's more general model.

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Robin Pemantle. 2004-04-05. Cycles in random k-ary maps and the poor performance of random random number generation. https://arxiv.org/abs/math/0404103

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