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1 results

  • Hendricks libraries and Tsetlin piles

  • Jacques-Edouard Dies
  • Journal:
    Advances in Applied Probability / Volume 14 / Issue 1 / March 1982
    Published online by Cambridge University Press:
    01 July 2016, pp. 37-55
    Print publication:
    March 1982

  • In order to study the transience of Hendricks libraries, we introduce and study a special class of Markov chains, the Tsetlin d-piles, generalizing Tsetlin libraries and briefly defined as follows: a 1-pile is a Tsetlin library and a d-pile is a Tsetlin library where each book is replaced by a (d − 1)-pile. We give a stationary measure of these chains and establish the necessary and sufficient conditions for positive recurrence and transience. Finally, the study of d-piles allows us to determine a sufficient condition for transience of quite a large class of Hendricks libraries.