The phase transition for domination in two interacting urns with power reinforcement

2026/07/24 by Jiaming Xia
#math.PR

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Abstract

We study two interacting urns with power reinforcement W(n)=n^α, for α>1. Using Qin's stochastic-approximation theorem as input, we reduce the phase transition problem for domination to the sign analysis of a single analytic function Φ_p. This deterministic reduction identifies the sharp threshold and proves that the two natural critical parameters for domination coincide.

Related

• Interacting urn models with strong reinforcement
• Phase transitions in non-linear urns with interacting types
• Urn models with two types of strategies
• Generalized Interacting Urn Models
• Fluctuation Theorems for Synchronization of Interacting Polya's urns