Regenerative tree growth processes
نویسندگان
چکیده
We introduce regenerative tree growth processes as consistent families of random trees with n labelled leaves, n ≥ 1, with a regenerative property at branch points. We establish necessary and sufficient conditions on the growth rules under which we can apply results by Haas and Miermont to establish self-similar random trees and residual mass processes as scaling limits. This framework includes all growth processes for exchangeably labelled Markov branching trees, as well as non-exchangeable models such as the alpha-theta model, the alpha-gamma model and all restricted exchangeable models previously studied. A key result is a representation of the growth rules with a σ-finite dislocation measure extending Bertoin’s notion of an exchangeable dislocation measure from the setting of homogeneous fragmentations. AMS 2000 subject classifications: 60J80.
منابع مشابه
Regenerative tree growth: structural results and convergence
We introduce regenerative tree growth processes as consistent families of random trees with n labelled leaves, n ≥ 1, with a regenerative property at branch points. This framework includes growth processes for exchangeably labelled Markov branching trees, as well as nonexchangeable models such as the alpha-theta model, the alpha-gamma model and all restricted exchangeable models previously stud...
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