具有噪声交互的非线性意见动力学的相变
Phase Transition of a Non-Linear Opinion Dynamics with Noisy Interactions
AI总结：
本文为二元 undecided dynamics 引入均匀消息噪声，证明亚稳态共识在 p=1/6 处发生相变，并将其等价于含固执智能体的模型。
摘要：
在若干真实的多智能体系统（MAS）中，人们观察到只能实现较弱形式的亚稳态共识：绝大多数智能体就某种意见达成一致，而其他意见仍由少数智能体继续支持。在本工作中，我们通过研究二元设置下著名的 undecided dynamics，朝着考察复杂（非线性）意见动力学中的亚稳态共识迈出一步；已知该动力学会比 voter dynamics 以指数级更快地达成共识。我们提出一种简单形式的均匀噪声，其中每条消息都能以概率 p 变成另一条消息，并证明亚稳态共识的持续性在 p=1/6 处经历相变。具体而言，在该阈值以下，我们证明系统以高概率进入一个亚稳态区间，在该区间中，绝大多数智能体在多项式时间内持续支持同一意见。此外，只要初始偏差略大于其标准差，这一意见恰好就是初始多数意见。相反，在阈值以上，我们表明，即使初始偏差达到最大，关于初始多数意见的信息也会在对数时间内“丢失”。有趣的是，利用一个简单的耦合论证，我们证明上述噪声模型与一部分智能体表现得固执的模型等价。
英文摘要：
In several real \emph{Multi-Agent Systems} (MAS), it has been observed that only weaker forms of\emph{metastable consensus} are achieved, in which a large majority of agents agree on some opinion while other opinions continue to be supported by a (small) minority of agents. In this work, we take a step towards the investigation of metastable consensus for complex (non-linear) \emph{opinion dynamics} by considering the famous \undecided dynamics in the binary setting, which is known to reach consensus exponentially faster than the \voter dynamics. We propose a simple form of uniform noise in which each message can change to another one with probability $p$ and we prove that the persistence of a \emph{metastable consensus} undergoes a \emph{phase transition} for $p=\frac 16$. In detail, below this threshold, we prove the system reaches with high probability a metastable regime where a large majority of agents keeps supporting the same opinion for polynomial time. Moreover, this opinion turns out to be the initial majority opinion, whenever the initial bias is slightly larger than its standard deviation.On the contrary, above the threshold, we show that the information about the initial majority opinion is "lost" within logarithmic time even when the initial bias is maximum.Interestingly, using a simple coupling argument, we show the equivalence between our noisy model above and the model where a subset of agents behave in a \emph{stubborn} way.
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。
