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Single-shelf library-type Markov chains with infinitely many books

Published online by Cambridge University Press:  14 July 2016

Peter R. Nelson
Peter R. Nelson*
Affiliation:
Ohio State University
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Abstract

In a single-shelf library having infinitely many books B1, B2, …, the probability of selecting each book is assumed known. Books are removed one at a time and replaced in position k prior to the next removal. Books are moved either to the right or the left as is necessary to vacate position k. Those arrangements of books where after some finite position all the books are in natural order (book i occupies position i) are considered as states in an infinite Markov chain. When k > 1, we show that the chain can never be positive recurrent. When k = 1, we find the limits of ratios of one-step transition probabilities; and when k = 1 and the chain is transient, we find the Martin exit boundary.

Keywords

MARKOV CHAINSRATIO LIMIT THEOREMSMARTIN EXIT BOUNDARY
Type
Research Papers
Information
Journal of Applied Probability , Volume 14 , Issue 2 , June 1977 , pp. 298 - 308
Copyright
Copyright © Applied Probability Trust 1977 

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References

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