Size-biased diffusion limits for the inclusion process
A talk in the Oberseminar Wahrscheinlichkeitstheorie series by
Stefan Großkinsky
| Abstract: | We study the Inclusion Process with vanishing diffusion coefficient,
which is known to exhibit condensation and metastable dynamics for
cluster locations. Here we focus on the dynamics of mass distribution
rather than locations, and consider the process on the complete graph
in the thermodynamic limit with fixed particle density. We describe
the mass distribution for a given configuration by a measure on a
suitably scaled mass space and derive a limiting measure-valued
process. When the diffusion coefficient scales like the inverse of the
system size, the scaling limit is equivalent to the well known
Poisson-Dirichlet diffusion, offering an alternative point of view for
this well-established dynamics. Our approach can be generalized to
other scaling regimes, providing a natural extension of the
Poisson-Dirichlet diffusion to infinite mutation rate. Considering
size-biased mass distributions, our approach yields an interesting
characterization of the limiting dynamics via duality.
This is joint work with Simon Gabriel and Paul Chleboun (both Warwick). Within the CRC this talk is associated to the project(s): B10 |