Self Organization of Interacting Polya Urns

TL;DR

This paper presents a new model of interacting Polya urns exhibiting self-organized criticality, with complex stationary states and critical phases, supported by extensive simulations across various dimensions.

Contribution

It introduces a novel model of interacting Polya urns with self-organized critical properties, including non-homogeneous stationary states and non-trivial exponents.

Findings

Presence of a non-homogeneous stationary state

Existence of a non-stationary critical phase

Non-trivial exponents even in mean field

Abstract

We introduce a simple model which shows non-trivial self organized critical properties. The model describes a system of interacting units, modelled by Polya urns, subject to perturbations and which occasionally break down. Three equivalent formulations - stochastic, quenched and deterministic - are shown to reproduce the same dynamics. Among the novel features of the model are a non-homogeneous stationary state, the presence of a non-stationary critical phase and non-trivial exponents even in mean field. We discuss simple interpretations in term of biological evolution and earthquake dynamics and we report on extensive numerical simulations in dimensions $d=1,2$ as well as in the random neighbors limit.