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

Abstract

We study two interacting urns with power reinforcement $W(n)=n^{\hat{I}}\pm$, for $\hat{I}\pm >1$. 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 $\hat{I}{¦}_p$. This deterministic reduction identifies the sharp threshold and proves that the two natural critical parameters for domination coincide.

18 pages, 3 figures