Abstract In (Combin. Probab. Comput. 9 (2000) 191–204), Aldous investigates a symmetric
Markov chain on cladograms and gives bounds on its mixing and relaxation times. The latter …

Abstract The Ray–Knight theorems show that the local time processes of various path
fragments derived from a one-dimensional Brownian motion B are squared Bessel …

Electron. J. Probab. 25 (2020), article no. 133, https://doi.org/10.1214/20-EJP521 Page 1 E
lectro n i c J o u r nal o f P r o b ability Electron. J. Probab. 25 (2020), article no. 133, 1–46. ISSN …

The Aldous diffusion is a conjectured Markov process on the space of real trees that is the
continuum analogue of discrete Markov chains on binary trees. We construct this …

Previous work constructed Fleming–Viot-type measure-valued diffusions (and diffusions on
a space of interval partitions of the unit interval $[0, 1] $) that are stationary with respect to …

We study composition-valued continuous-time Markov chains that appear naturally in the
framework of Chinese Restaurant Processes (CRPs). As time evolves, new customers arrive …

We give a pathwise construction of a two-parameter family of purely-atomic-measure-valued
diffusions in which ranked masses of atoms are stationary with the Poisson–Dirichlet (α, θ) …

We introduce and study interval partition diffusions with Poisson–Dirichlet (α, θ) stationary
distribution for parameters α∈(0, 1) and θ≥ 0. This extends previous work on the cases (α …

We establish two results about local times of spectrally positive stable processes. The first is
a general approximation result, uniform in space and on compact time intervals, in a model …

Motivated by a down-up Markov chain on cladograms, David Aldous conjectured in 1999
that there exists a" diffusion on continuum trees" whose mass partitions at any finite number …