Critical P\'olya urn

TL;DR

This paper introduces a modified Pólya urn model with dynamic suppression and enhancement mechanisms, leading to self-organized criticality and scale invariance, with implications for understanding universality classes in avalanche phenomena.

Contribution

It presents a novel variant of the Pólya urn process incorporating stochastic control of growth and dormancy, revealing critical behavior and universality classes.

Findings

Model exhibits scale invariance and criticality.

Different versions of the model show varied universality classes.

Mechanism relates to neural network dynamics.

Abstract

We propose a variant model of P{\'o}lya urn process, where the dynamics consist of two competing elements namely, suppression of growth and enhancement of dormant character. Here the level of such features are controlled by an internal parameter in a random manner, so as the system self-organizes and characteristic observables exhibit scale invariance suggesting the existence of criticality. Varying the internal control parameter, one can explain interesting universality classes for avalanche-type events. We also discuss different versions of the model. It is pointed that such an underlying mechanism has earlier been noted to operate in a neural network.