投票者模型的动态噪声敏感性

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2021-11-24 DOI:10.1214/22-ECP483

Gideon Amir, Omer Angel, Rangel Baldasso, R. Peretz

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引用次数: 0

摘要

我们研究了选民模型在有限图上的一致意见如何随着噪声敏感性的变化而变化，涉及初始意见和动力学。我们首先证明，对于初始配置的小扰动，最终意见是稳定的。当在控制过程演变的动力学中引入扰动时，会观察到不同的影响，在这种情况下，最终意见是噪声敏感的。我们的证明依赖于选民模型和凝聚随机行走之间的关系，以及当我们具有耦合动力学时对这种进化的精确描述。

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Dynamical noise sensitivity for the voter model

We study how the consensus opinion of the voter model on ﬁnite graphs varies in light of noise sensitivity with respect to both the initial opinions and the dynamics. We ﬁrst prove that the ﬁnal opinion is stable with respect to small perturbations of the initial conﬁguration. Diﬀerent eﬀects are observed when a perturbation is introduced in the dynamics governing the evolution of the process, and the ﬁnal opinion is noise sensitive in this case. Our proofs rely on the relationship between the voter model and coalescing random walks, and on a precise description of this evolution when we have coupled dynamics.

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来源期刊

Electronic Communications in Probability 工程技术-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.