Skip to main content
Open Access Publications from the University of California

UC Berkeley

UC Berkeley Previously Published Works bannerUC Berkeley

Inhomogeneous continuum random trees and the entrance boundary of the additive coalescent


Regard an element of the set of ranked discrete distributions Δ := {(x1, x2,. . .) : x1 ≥ x2 ≥ . . . ≥ 0. Σi xi = 1} as a fragmentation of unit mass into clusters of masses xi. The additive coalescent is the Δ-valued Markov process in which pairs of clusters of masses {xi, xj}merge into a cluster of mass xi + xj at rate xi + xj. Aldous and Pitman (1998) showed that a version of this process starting from time -∞ with infinitesimally small clusters can be constructed from the Brownian continuum random tree of Aldous (1991, 1993) by Poisson splitting along the skeleton of the tree. In this paper it is shown that the general such process may be constructed analogously from a new family of inhomogeneous continuum random trees.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View