On Knuth's generalization of Banach's matchbox problem

W.M.B. Dukes, Ken Duffy

Research output: Contribution to journalArticlepeer-review


We revisit a simply stated problem of 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.
Original languageEnglish
Pages (from-to)107-118
Number of pages12
JournalMathematical Proceedings of the Royal Irish Academy
Issue number1
Publication statusPublished - Nov 2004


  • Knuth
  • Banach's matchbox problem
  • large deviation principles


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