Markov chains on graded posets: Compatibility of up-directed and down-directed transition probabilities
(English)In: Order, ISSN 0167-8094, E-ISSN 1572-9273, ISSN 0167-8094Article in journal (Refereed) Accepted
We consider two types of discrete-time Markov chains where thestate space is a graded poset and the transitionsare taken along the covering relations in the poset. The first type of Markov chain goes only in one direction, either up or down in the poset (an up chain or down chain). The second type toggles between two adjacent rank levels (an up-and-down chain). We introduce two compatibility concepts between the up-directed transition probabilities (an up rule) and the down-directed(a down rule), and we relate these to compatibility betweenup-and-down chains. This framework is used to prove a conjecture about a limit shape for a process on Young's lattice. Finally, we settle the questions whether the reverse of an up chain is a down chain for some down rule and whether there exists an up or down chain at all if the rank function is not bounded.
Place, publisher, year, edition, pages
Graded poset, Markov chain, Young diagram, Young's lattice, Limit shape
Research subject Mathematics/Applied Mathematics
IdentifiersURN: urn:nbn:se:mdh:diva-35015OAI: oai:DiVA.org:mdh-35015DiVA: diva2:1081145
FunderSwedish Research Council, 2010-5565, 621-2009-6090