## Interacting Urn Schemes

In this talk we will introduce a new model of "interactive urns" with the goal of obtaining a limiting distribution, which may then be considered as an example of a model exhibiting the phenomenon known as "self-organized criticality (SOC)" in statistical physics literature. We will show that if the interactions are defined locally on a finite or infinite network which is a Directed Acyclic Graph (DAG) with no vertex having an infinite line of descent, then limit exists for fairly general class of replacements including Pólya-type replacements. We will also show that the limit may be described as a solution of a Dirichlet Problem on an appropriate space of finite measures. If time permits, we will also indicate what happens if the under lying network has vertices with infinite line of descent. [This is a joint work with my current Ph.D. student Mr. Deborshi Das]

Area: CS40 - Recent developments for urn models (Andrea Ghiglietti and Giacomo Aletti)

Keywords: Interacting urn models, Polya urn scheme, self-organized criticality

*Il paper è coperto da copyright.*