We analyze average-based distributed algorithms relying on simple and pairwise random interactions among a large and unknown number of anonymous agents. This allows the characterization of global properties emerging from these local interactions. Agents start with an initial integer value, and at each interaction keep the average integer part of both values as their new value. The convergence occurs when, with high probability, all the agents possess the same value, which means that they all know a property of the global system. Using a well-chosen stochastic coupling, we improve upon existing results by providing explicit and tight bounds on the convergence time. We apply these general results to both the proportion problem and the system size problem.

中文翻译：

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基于平均值的分布式算法的随机分析

我们分析了基于平均值的分布式算法，该算法依赖于大量未知数量的匿名代理之间的简单和成对随机交互。这允许表征从这些局部相互作用中出现的全局属性。代理以初始整数值开始，并且在每次交互时将两个值的平均整数部分保持为新值。当所有智能体很有可能拥有相同的值时，就会发生收敛，这意味着它们都知道全局系统的一个属性。使用精心挑选的随机耦合，我们通过在收敛时间上提供明确和严格的界限来改进现有结果。我们将这些一般结果应用于比例问题和系统规模问题。