Publications (73)
Gibbs distributions for random partitions generated by a fragmentation process
Nathanael Berestycki, Jim Pitman
In this paper we study random partitions of 1,...n, where every cluster of size j can be in any of w\_j possible internal states. The Gibbs (n,k,w) distribution is obtained by samp…
Gaps and interleaving of point processes in sampling from a residual allocation model
Jim Pitman, Yuri Yakubovich
This article presents a limit theorem for the gaps between order statistics of a sample of size f…
Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees
David J. Aldous, Gregory Miermont, Jim Pitman
We study the asymptotics of the -mapping model of random mappings on as gets large, under a large class of asymptotic regimes for the underlying distribution . We e…
One-dimensional Brownian particle systems with rank dependent drifts
Soumik Pal, Jim Pitman
We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our mai…
Hidden symmetries and limit laws in the extreme order statistics of the Laplace random walk
Jim Pitman, Wenpin Tang
This paper is concerned with the limit laws of the extreme order statistics derived from a symmetric Laplace walk. We provide two different descriptions of the point process of the…
Extreme order statistics of random walks
Jim Pitman, Wenpin Tang
This paper is concerned with the limit theory of the extreme order statistics derived from random walks. We establish the joint convergence of the order statistics near the minimum…