Stochastic coalescence multi-fragmentation processes

Stochastic Coalescence Multi-Fragmentation Processes

Exchangeable Fragmentation-Coalescence processes and their equilibrium measures

We define and study a family of Markov processes with state space the compact set of all partitions of N that we call exchangeable fragmentation-coalescence processes. They can be viewed as a combination of exchangeable fragmentation as defined by Bertoin and of homogenous coalescence as defined by Pitman and Schweinsberg or Möhle and Sagitov. We show that they admit a unique invariant probabil...

Two-Parameter Poisson-Dirichlet Measures and Reversible Exchangeable Fragmentation-Coalescence Processes

We show that for 0 < α < 1 and θ > −α, the Poisson-Dirichlet distribution with parameter (α, θ) is the unique reversible distribution of a rather natural fragmentation-coalescence process. This completes earlier results in the literature for certain split and merge transformations and the parameter α = 0. DOI: https://doi.org/10.1017/S0963548307008784 Posted at the Zurich Open Repository and Ar...

Stochastic ballistic annihilation and coalescence

We study a class of stochastic ballistic annihilation and coalescence models with a binary velocity distribution in one dimension. We obtain an exact solution for the density which reveals a universal phase diagram for the asymptotic density decay. By universal we mean that all models in the class are described by a single phase diagram spanned by two reduced parameters. The phase diagram revea...

Stochastic coalescence in logarithmic time

The following distributed coalescence protocol was introduced by Dahlia Malkhi in 2006 motivated by applications in social networking. Initially there are n agents wishing to coalesce into one cluster via a decentralized stochastic process, where each round is as follows: Every cluster flips a fair coin to dictate whether it is to issue or accept requests in this round. Issuing a request amount...