Upward and Downward Runs on Partially Ordered Sets

Details Upward and Downward Runs on Partially Ordered Sets Upward and Downward Runs on Partially Ordered Sets

2008-10-13

arxiv.org/abs/0810.2289v2

Mathematics

Probability

13 pages

Scientific paper

We consider Markov chains on partially ordered sets that generalize the
success-runs and remaining life chains in reliability theory. We find
conditions for recurrence and transience and give simple expressions for the
invariant distributions. We study a number of special cases, including rooted
trees, uniform posets, and posets associated with positive semigroups.

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