Distribution of consensus in a broadcast-based consensus algorithm with random initial opinions

【Author】 Shioda, Shigeo; Kato, Dai

【Source】JOURNAL OF APPLIED PROBABILITY

【影响因子】1.116

【Abstract】We study the distribution of the consensus formed by a broadcast-based consensus algorithm for cases in which the initial opinions of agents are random variables. We first derive two fundamental equations for the time evolution of the average opinion of agents. Using the derived equations, we then investigate the distribution of the consensus in the limit in which agents do not have any mutual trust, and show that the consensus without mutual trust among agents is in sharp contrast to the consensus with complete mutual trust in the statistical properties if the initial opinion of each agent is integrable. Next, we provide the formulation necessary to mathematically discuss the consensus in the limit in which the number of agents tends to infinity, and derive several results, including a central limit theorem concerning the consensus in this limit. Finally, we study the distribution of the consensus when the initial opinions of agents follow a stable distribution, and show that the consensus also follows a stable distribution in the limit in which the number of agents tends to infinity.

【Keywords】Stable distribution; central limit theorem; Cauchy; Gaussian; Levy

【发表时间】2023 2023 MAY 9

【收录时间】2023-06-05

【文献类型】理论模型

【主题类别】

区块链技术-核心技术-共识机制