TY - JOUR
A1 - Evans, Steven Neil
A1 - Grübel, Rudolf
A1 - Wakolbinger, Anton
T1 - Trickle-down processes and their boundaries
T2 - Electronic journal of probability
N2 - 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 q-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 compactifications, Poisson boundaries and tail σ-fields.
KW - harmonic function
KW - h-transform
KW - σ-field
KW - Poisson boundary
KW - internal diffusion limited aggregation
KW - binary search tree
KW - digital search tree
KW - Dirichlet random measure
KW - random recursive tree
KW - Chinese restaurant process
KW - random partition
KW - Ewens sampling formula
KW - Griffiths–Engen–McCloskey distribution
KW - Mallows model
KW - q-binomial theorem
KW - Catalan number
KW - composition
KW - quincunx
Y1 - 2012
UR - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32896
UR - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-328962
SN - 1083-6489
VL - 17
IS - 1
SP - 1
EP - 58
PB - EMIS ELibEMS
CY - [Madralin]
ER -