Size-biased diffusion limits and the inclusion process
arXiv:2304.09722 · doi:10.1214/24-EJP1119
Abstract
We consider the inclusion process on the complete graph with vanishing diffusivity, which leads to condensation of particles in the thermodynamic limit. Describing particle configurations in terms of size-biased and appropriately scaled empirical measures of mass distribution, we establish convergence in law of the inclusion process to a measure-valued Markov process on the space of probability measures. In the case where the diffusivity vanishes like the inverse of the system size, the derived scaling limit is equivalent to the well known Poisson-Dirichlet diffusion, offering an alternative viewpoint on these well-established dynamics. Moreover, our approach covers all scaling regimes of the system parameters and yields a natural extension of the Poisson-Dirichlet diffusion to infinite mutation rate. We also discuss in detail connections to known results on related Fleming-Viot processes.
37 pages, minor changes, Accepted for publication in Electron. J. Probab
References in corpus (19)
- Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
- Duality and exact correlations for a model of heat conduction
- Duality for stochastic models of transport
- Condensation in the inclusion process and related models
- Spatial random permutations and Poisson-Dirichlet law of cycle lengths
- Condensation in stochastic particle systems with stationary product measures
- Dynamics of condensation in the symmetric inclusion process
- Explosive condensation in a mass transport model
- Condensation in the inhomogeneous zero-range process: an interplay between interaction and diffusion disorder
- Metastability in the reversible inclusion process
- Smoothness and asymptotic estimates of densities for SDEs with locally smooth coefficients and applications to square root-type diffusions
- Dynamics of condensation in the totally asymmetric inclusion process
- Metastability in a condensing zero-range process in the thermodynamic limit
- Wright-Fisher construction of the two-parameter Poisson-Dirichlet diffusion
- Condensation and Metastable Behavior of Non-reversible Inclusion Processes
- Structure of the condensed phase in the inclusion process
- Derivation of mean-field equations for stochastic particle systems
- Explosive condensation in symmetric mass transport models
- Split-and-Merge in Stationary Random Stirring on Lattice Torus