58 citations · 309 across the 33 of their papers we have counts for
38 papers · 1 filter
Mass erasure on measured -trees, applications to Lévy forests
Thomas Duquesne, Matthias Winkel
Let . For a complete and separable -tree equipped with a root and a finite Borel measure , we define the -mass-erased tree by removing from a…
The Aldous diffusion: a stationary evolution of the Brownian CRT
Noah Forman, Soumik Pal, Douglas Rizzolo +1
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 of…
Ranked masses in two-parameter Fleming-Viot diffusions
Noah Forman, Soumik Pal, Douglas Rizzolo +1
In previous work, we constructed Fleming--Viot-type measure-valued diffusions (and diffusions on a space of interval partitions of the unit interval ) that are stationary wi…
Up-down ordered Chinese restaurant processes with two-sided immigration, emigration and diffusion limits
Quan Shi, Matthias Winkel
We establish scaling limit theorems for the up-down ordered Chinese restaurant processes (oCRPs) of Rogers and Winkel as processes in a space of interval partitions. As previously…
Two-sided immigration, emigration and symmetry properties of self-similar interval partition evolutions
Quan Shi, Matthias Winkel
Forman et al. (2020+) constructed -interval partition evolutions for and , in which the total sums of interval lengths ("total mass") evolve as squared B…
Diffusions on a space of interval partitions: The two-parameter model
Noah Forman, Douglas Rizzolo, Quan Shi +1
We introduce and study interval partition diffusions with Poisson--Dirichlet stationary distribution for parameters and . This extends previous work on t…