We study a variant of branching Markov chains in which the branching is governed by a fixed deterministic tree $T$ rather than a Galton-Watson process. Sample path properties of these chains are determined by an interplay of the tree structure and the transition probabilities. For instance, there exists an infinite path in $T$ with a bounded trajectory iff the Hausdorff dimension of $T$ is greater than $\log(1/\rho)$ where $\rho$ is the spectral radius of the transition matrix.
Publié le : 1994-01-14
Classification:
Trees,
Markov chains,
branching random walks,
recurrence,
Hausdorff dimension,
packing dimension,
60J15,
60J10,
60J80
@article{1176988857,
author = {Benjamini, Itai and Peres, Yuval},
title = {Markov Chains Indexed by Trees},
journal = {Ann. Probab.},
volume = {22},
number = {4},
year = {1994},
pages = { 219-243},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988857}
}
Benjamini, Itai; Peres, Yuval. Markov Chains Indexed by Trees. Ann. Probab., Tome 22 (1994) no. 4, pp. 219-243. http://gdmltest.u-ga.fr/item/1176988857/