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arXiv · 0810.2289

Upward and Downward Runs on Partially Ordered Sets

Kyle Siegrist
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Abstract

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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Kyle Siegrist. 2010-04-06. Upward and Downward Runs on Partially Ordered Sets. https://arxiv.org/abs/0810.2289

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