Erdös-Rényi图上的约束信息传递
Constrained information transmission on Erdös-Rényi graphs
摘要：
我们在Erdös-Rény随机图上用参数$(n,p)$和有限的资源对消息的信息传输进行建模。图的顶点表示可以随机广播消息的服务器。每个服务器都有一个随机的排放资本，每次排放减少1。我们研究两个自然的动态：在第一个动态，知情的服务器执行其尝试，然后在他们每个检查，如果相应的边缘是开放的或没有;在第二个动态的知情的服务器知道一个先验谁是它的邻居，它执行所有的尝试，其实际的邻居在图中。在每种情况下，我们得到一阶和二阶渐近（大数定律和中心极限定理），当$n\to \infty$和$p$是固定的，为最终比例的通知服务器。
英文摘要：
We model the transmission of information of a message on the Erdös-Rény random graph with parameters $(n,p)$ and limited resources. The vertices of the graph represent servers that may broadcast a message at random. Each server has a random emission capital that decreases by one at each emission. We examine two natural dynamics: in the first dynamics, an informed server performs its attempts, then checks at each of them if the corresponding edge is open or not; in the second dynamics the informed server knows a priori who are its neighbors, and it performs all its attempts on its actual neighbors in the graph. In each case, we obtain first and second order asymptotics (law of large numbers and central limit theorem), when $n\to \infty$ and $p$ is fixed, for the final proportion of informed servers.
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。
