58 citations · 309 across the 33 of their papers we have counts for
5 papers · 1 filter
A recursive distribution equation for the stable tree
Nicholas Chee, Franz Rembart, Matthias Winkel
We provide a new characterisation of Duquesne and Le Gall's -stable tree, , as the solution of a recursive distribution equation (RDE) of the form $\mathcal{T}\overse…
Aldous diffusion I: a projective system of continuum -tree evolutions
Noah Forman, Soumik Pal, Douglas Rizzolo +1
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 conjectu…
Squared Bessel processes of positive and negative dimension embedded in Brownian local times
Jim Pitman, Matthias Winkel
The Ray--Knight theorems show that the local time processes of various path fragments derived from a one-dimensional Brownian motion are squared Bessel processes of dimensions…
Interval partition evolutions with emigration related to the Aldous diffusion
Noah Forman, Soumik Pal, Douglas Rizzolo +1
We construct a stationary Markov process corresponding to the evolution of masses and distances of subtrees along the spine from the root to a branch point in a conjectured station…
Projections of the Aldous chain on binary trees: Intertwining and consistency
Noah Forman, Soumik Pal, Douglas Rizzolo +1
Consider the Aldous Markov chain on the space of rooted binary trees with labeled leaves in which at each transition a uniform random leaf is deleted and reattached to a unifor…