On Knuth’s generalization of Banach’s Matchbox problem

Duffy, K. and Dukes, W.M.B. (2002) On Knuth’s generalization of Banach’s Matchbox problem. (Preprint)

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Abstract

We revisit a simply stated problem by Knuth. Previous approaches rely on the Bernoulli nature of the underlying stochastic process to recover the systems mean behaviour. We show that limiting results hold for a wide range of stochastic processes. A Large Deviation Principle (LDP) is proved, allowing estimates to be made for the probability of rare-events. From the LDP, a weak law of large numbers is deduced.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 13 Jun 2018 14:29
Last Modified: 17 Jul 2018 10:32
URI: http://dair.dias.ie/id/eprint/454

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