Replica Analysis of Preferential Urn Model

Abstract

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