Trickle-down processes and their boundaries

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dc.identifier.uri Evans, Steven N. Grübel, Rudolf Wakolbinger, Anton 2017-04-21T09:47:40Z 2017-04-21T09:47:40Z 2012
dc.identifier.citation Evans, S.N.; Grübel, R.; Wakolbinger, A.: Trickle-down processes and their boundaries. In: Electronic Journal of Probability 17 (2012), S. 1-58. DOI:
dc.description.abstract It is possible to represent each of a number of Markov chains as an evolving sequence of connected subsets of a directed acyclic graph that grow in the following way: initially, all vertices of the graph are unoccupied, particles are fed in one-by-one at a distinguished source vertex, successive particles proceed along directed edges according to an appropriate stochastic mechanism, and each particle comes to rest once it encounters an unoccupied vertex. Examples include the binary and digital search tree processes, the random recursive tree process and generalizations of it arising from nested instances of Pitman's two-parameter Chinese restaurant process, tree-growth models associated with Mallows' φ model of random permutations and with Schützenberger's non-commutative g-binomial theorem, and a construction due to Luczak and Winkler that grows uniform random binary trees in a Markovian manner. We introduce a framework that encompasses such Markov chains, and we characterize their asymptotic behavior by analyzing in detail their Doob-Martin com-pactifications, Poisson boundaries and tail cr-fields. eng
dc.language.iso eng
dc.publisher Beachwood, OH : Institute of Mathematical Statistics
dc.relation.ispartofseries Electronic Journal of Probability 17 (2012)
dc.rights CC BY 3.0 Unported
dc.subject Binary search tree eng
dc.subject Catalan number eng
dc.subject Chinese restaurant process eng
dc.subject Composition eng
dc.subject Digital search tree eng
dc.subject Dirichlet random measure eng
dc.subject E wens sampling formula eng
dc.subject Griffiths-engen-mccloskey distribution eng
dc.subject h-transform eng
dc.subject Harmonic function eng
dc.subject Internal diffusion limited aggregation eng
dc.subject Mallows model eng
dc.subject Poisson boundary eng
dc.subject q-binomial theorem eng
dc.subject Quincunx eng
dc.subject Random partition eng
dc.subject Random recursive tree eng
dc.subject Tail σ-field eng
dc.subject eng
dc.subject.ddc 510 | Mathematik ger
dc.title Trickle-down processes and their boundaries eng
dc.type article
dc.type Text
dc.relation.issn 1083-6489
dc.bibliographicCitation.volume 17
dc.bibliographicCitation.firstPage 1
dc.bibliographicCitation.lastPage 58
dc.description.version publishedVersion
tib.accessRights frei zug�nglich

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