Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Markov Chains on Graded Posets Compatibility of Up-Directed and Down-Directed Transition Probabilities
Malardalen Univ, Sch Educ Culture & Commun, Box 883, S-72123 Vasteras, Sweden..
Malardalen Univ, Sch Educ Culture & Commun, Box 883, S-72123 Vasteras, Sweden..
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2018 (English)In: Order, ISSN 0167-8094, E-ISSN 1572-9273, Vol. 35, no 1, p. 93-109Article in journal (Refereed) Published
Abstract [en]

We consider two types of discrete-time Markov chains where the state space is a graded poset and the transitions are 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 between up-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
SPRINGER , 2018. Vol. 35, no 1, p. 93-109
Keywords [en]
Graded poset, Markov chain, Young diagram, Young's lattice, Limit shape
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-225734DOI: 10.1007/s11083-016-9420-1ISI: 000427496600006Scopus ID: 2-s2.0-85017160313OAI: oai:DiVA.org:kth-225734DiVA, id: diva2:1196505
Funder
Swedish Research Council, 2010-5565; 621-2009-6090
Note

QC 20180410

Available from: 2018-04-10 Created: 2018-04-10 Last updated: 2018-04-10Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Sjöstrand, Jonas
By organisation
Mathematics (Dept.)
In the same journal
Order
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf