Stochastic gel-shatter cycles in coalescence-fragmentation models

Stochastic Coalescence Multi-Fragmentation Processes

Mixing times for random k-cycles and coalescence-fragmentation chains

Let Sn be the permutation group on n elements, and consider a random walk on Sn whose step distribution is uniform on k-cycles. We prove a well-known conjecture that the mixing time of this process is (1/k)n logn, with threshold of width linear in n. Our proofs are elementary and purely probabilistic, and do not appeal to the representation theory of Sn. CMS Wilberforce Rd., Cambridge Universit...

Explosion Phenomena in Stochastic Coagulation – Fragmentation Models

First we establish explosion criteria for jump processes with an arbitrary locally compact separable metric state space. Then these results are applied to two stochastic coagulation–fragmentation models— the direct simulation model and the mass flow model. In the pure coagulation case, there is almost sure explosion in the mass flow model for arbitrary homogeneous coagulation kernels with expon...

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...

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...