帝国与渗流：相邻区域的随机合并
Empires and Percolation: Stochastic Merging of Adjacent Regions
摘要：
我们介绍了一个随机模型，相邻的平面区域$A, B$合并stocheros在一定的速度$λ(A,B)$，并观察类比的平均场凝聚和键渗流的研究课题。在有限的时间里会出现无限的区域吗？我们在$λ$上给出了一个简单的条件，使{ \em霸权}属性成立，另一个简单的条件使它不成立，但这些条件之间存在很大的差距，其中包括$λ(A,B) \equiv 1$的情况。在这种情况下，一个非严格的分析论证和模拟表明霸权。
英文摘要：
We introduce a stochastic model in which adjacent planar regions $A, B$ merge stochastically at some rate $λ(A,B)$, and observe analogies with the well-studied topics of mean-field coagulation and of bond percolation. Do infinite regions appear in finite time? We give a simple condition on $λ$ for this {\em hegemony} property to hold, and another simple condition for it to not hold, but there is a large gap between these conditions, which includes the case $λ(A,B) \equiv 1$. For this case, a non-rigorous analytic argument and simulations suggest hegemony.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
