The inclusion process is a stochastic particle system in which attractive interactions can lead to particle clusters of diverging size, when taking a thermodynamic limit, i.e. zooming out. This phenomenon is known as condensation. Our aim is to study the limiting dynamics of such a process, where on top of attractive particle interactions, we also consider (vanishing) mean-field random walk interactions.
We shall see that the limiting dynamics depend on the explicit strength of the random walk interactions. It turns out both useful and insightful to embed particle configurations into the space of probability measures in a size-biased fashion. This allows us to recover an equivalent version of a well known scaling limit, the infinitely-many-neutral-alleles model, and extend the scaling behaviour to the case of slowly vanishing random walk interactions.
The talk is based on joint work with Paul Chleboun and Stefan Grosskinsky.
