115 citations · 485 across the 25 of their papers we have counts for
5 papers · 1 filter
Colored loop-erased random walk on the complete graph
Jomy Alappattu, Jim Pitman
Starting from a sequence regarded as a walk through some set of values, we consider the associated loop-erased walk as a sequence of directed edges, with an edge from to if…
Poisson representation of a Ewens fragmentation process
Alexander Gnedin, Jim Pitman
A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of at time is governed by the Ewe…
Continuum tree asymptotics of discrete fragmentations and applications to phylogenetic models
Bénédicte Haas, Grégory Miermont, Jim Pitman +1
Given any regularly varying dislocation measure, we identify a natural self-similar fragmentation tree as scaling limit of discrete fragmentation trees with unit edge lengths. As a…
Exchangeable partitions derived from Markovian coalescents
Rui Dong, Alexander Gnedin, Jim Pitman
Kingman derived the Ewens sampling formula for random partitions describing the genetic variation in a neutral mutation model defined by a Poisson process of mutations along lines…
Moments of convex distribution functions and completely alternating sequences
Alexander Gnedin, Jim Pitman
We solve the moment problem for convex distribution functions on in terms of completely alternating sequences. This complements a recent solution of this problem by Diaconi…