Replica analysis of a preferential urn model

TL;DR

This paper uses the replica method to analyze a stochastic preferential urn model with randomness, revealing that it exhibits a fat-tailed occupation distribution, which is relevant for complex networks and econophysics.

Contribution

It provides the first analytical replica-based analysis of a preferential urn model with randomness, demonstrating its fat-tailed distribution.

Findings

The model exhibits a fat-tailed occupation distribution.

Replica analysis clarifies the role of randomness in the model.

Results are applicable to complex networks and econophysics.

Abstract

We analyse a preferential urn model with randomness using the replica method. The preferential urn model is a stochastic model based on the concept "the rich get richer." The replica analysis clarifies that the preferential urn model with randomness shows a fat-tailed occupation distribution. The analytical treatments and results would be useful for various research fields such as complex networks, stochastic models, and econophysics.