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Markov chains on gr...
Markov chains on graded posets : Compatibility of up-directed and down-directed transition probabilities
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- Jonsson, Markus (författare)
- Mälardalens högskola,Utbildningsvetenskap och Matematik,MAM,Malardalen Univ, Sch Educ Culture & Commun, Box 883, S-72123 Vasteras, Sweden.
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- Kimmo, Eriksson (författare)
- Mälardalens högskola,Utbildningsvetenskap och Matematik,MAM,Malardalen Univ, Sch Educ Culture & Commun, Box 883, S-72123 Vasteras, Sweden.
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- Sjöstrand, Jonas (författare)
- KTH,Matematik (Inst.),Kungliga Tekniska Högskolan, Sweden
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(creator_code:org_t)
- 2017-04-08
- 2018
- Engelska.
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Ingår i: Order. - : Springer Netherlands. - 0167-8094 .- 1572-9273. ; :1, s. 93-109
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Graded poset
- Markov chain
- Young diagram
- Young's lattice
- Limit shape
- Mathematics/Applied Mathematics
- matematik/tillämpad matematik
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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