发表机构
Fudan University; Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（复旦大学; 上海数学与交叉学科研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究具有幂强化的两个相互作用瓮中支配的相变问题，以秦的随机逼近定理为基础，通过对解析函数\(\Phi_p\)的符号分析确定尖锐阈值，证明两个临界参数一致。
AI 中文摘要
我们研究了两个具有幂强化\(W(n)=n^\alpha\)（\(\alpha>1\)）的相互作用瓮。以秦的随机逼近定理为基础，我们将支配的相变问题简化为对单个解析函数\(\Phi_p\)的符号分析。这种确定性简化确定了尖锐阈值，并证明了支配的两个自然临界参数是一致的。
英文摘要
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. We determine the first-order behavior of the critical interaction parameter as $α\downarrow1$ and show that it is not nondecreasing in the reinforcement exponent, answering two questions posed by Qin.
Comments23 pages, 3 figures
