In this paper, we study the problem of achieving average consensus over a random time-varying sequence of directed graphs by extending the class of so-called push-sum algorithms to such random scenarios. Provided that an ergodicity notion, which we term the directed infinite flow property, holds and the auxiliary states of agents are uniformly bounded away from zero infinitely often, we prove the almost sure convergence of the evolutions of this class of algorithms to the average of initial states. Moreover, for a random sequence of graphs generated using a so-called time-varying B -irreducible probability matrix, we establish convergence rates for the proposed push-sum algorithm.

中文翻译：

---

随机图上的推和：几乎确定的收敛性和收敛率


在本文中，我们通过将所谓的推和算法类别扩展到此类随机场景来研究在随机时变有向图序列上实现平均共识的问题。假设遍历性概念（我们称之为有向无限流属性）成立，并且代理的辅助状态经常无限地一致地远离零，我们证明此类算法的演化几乎肯定会收敛于初始的平均值州。此外，对于使用所谓的时变 B 不可约概率矩阵生成的随机图序列，我们建立了所提出的推和算法的收敛率。