The convergence of the gossip process has been extensively studied; however, algorithms that generate a set of stochastic matrices, the infinite product of which converges to a rank-one matrix determined by a given weight vector, have been less explored. In this work, we propose an algorithm for constructing (local) stochastic matrices based on a given gossip network topology and a set of weights for averaging across different consensus clusters, ensuring that the gossip process converges to a finite limit set.

翻译：Gossip过程的收敛性已得到广泛研究；然而，生成一组随机矩阵（其无穷乘积收敛于由给定权重向量确定的秩一矩阵）的算法尚未得到充分探索。本研究提出一种基于给定Gossip网络拓扑结构和跨共识簇加权平均的权重集合来构建（局部）随机矩阵的算法，确保Gossip过程收敛至有限极限集。