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Digital Object Identifier (DOI) 10.1007/s00440-003-0334-7 Probab. Theory Relat. Fields 129, 182218 (2004)
 

Summary: Digital Object Identifier (DOI) 10.1007/s00440-003-0334-7
Probab. Theory Relat. Fields 129, 182­218 (2004)
David Aldous · GrŽegory Miermont · Jim Pitman
The exploration process of inhomogeneous
continuum random trees, and an extension
of Jeulin's local time identity
Received: 9 May 2003 / Revised version: 2 November 2003 /
Published online: 25 March 2004 ­ c Springer-Verlag 2004
Abstract. We study the inhomogeneous continuum random trees (ICRT) that arise as weak
limits of birthday trees. We give a description of the exploration process, a function defined
on [0, 1] that encodes the structure of an ICRT, and also of its width process, determining the
size of layers in order of height.These processes turn out to be transformations of bridges with
exchangeable increments, which have already appeared in other ICRT related topics such as
stochastic additive coalescence. The results rely on two different constructions of birthday
trees from processes with exchangeable increments, on weak convergence arguments, and
on general theory on continuum random trees.
1. Introduction
This paper completes one circle of ideas (describing the inhomogeneous continuum
random tree) while motivated by another (limits of non-uniform random p-map-
pings which are essentially different from the uniform case limit). Along the way,

  

Source: Aldous, David J. - Department of Statistics, University of California at Berkeley

 

Collections: Mathematics