论文标题
关于排水网络与分支的收敛
On the convergence of the drainage network with branching
论文作者
论文摘要
排水网络是一种融合随机步行的系统，在甘帕迪，罗伊和萨卡引入的凝聚前表现出长距离依赖。 Coletti，Fontes和Dias在扩散缩放下证明了其与Brownian Web的收敛。在这项工作中，我们引入了系统的扰动，该系统允许随机步行的分支，概率低概率随缩放参数而变化。当分支概率与缩放参数成反比时，我们表明该分支的排水网络由一个紧密的家族组成，因此任何弱极限点都包含一个布朗尼网络。我们推测，极限确实是布朗尼网络。
The Drainage Network is a system of coalescing random walks, exhibiting long-range dependence before coalescence, introduced by Gangopadhyay, Roy, and Sarkar. Coletti, Fontes, and Dias proved its convergence to the Brownian Web under diffusive scaling. In this work, we introduce a perturbation of the system allowing branching of the random walks with low probabilities varying with the scaling parameter. When the branching probability is inversely proportional to the scaling parameter, we show that this drainage network with branching consists of a tight family such that any weak limit point contains a Brownian Net. We conjecture that the limit is indeed the Brownian Net.
