Voter models on subcritical scale‐free random graphs

IF 0.9 3区数学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Random Structures & Algorithms Pub Date : 2022-07-23 DOI:10.1002/rsa.21107

J. Fernley, Marcel Ortgiese

引用次数: 2

Abstract

The voter model is a classical interacting particle system modelling how consensus is formed across a network. We analyze the time to consensus for the voter model when the underlying graph is a subcritical scale‐free random graph. Moreover, we generalize the model to include a “temperature” parameter controlling how the graph influences the speed of opinion change. The interplay between the temperature and the structure of the random graph leads to a very rich phase diagram, where in the different phases different parts of the underlying geometry dominate the time to consensus. Finally, we also consider a discursive voter model, where voters discuss their opinions with their neighbors. Our proofs rely on the well‐known duality to coalescing random walks and a detailed understanding of the structure of the random graphs.

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亚临界无标度随机图上的选民模型

选民模型是一个经典的相互作用粒子系统，它模拟了如何在网络中形成共识。我们分析了当底层图是一个亚临界无标度随机图时，选民模型的共识时间。此外，我们将模型推广到包含一个“温度”参数，以控制图如何影响意见变化的速度。温度和随机图结构之间的相互作用导致了一个非常丰富的相图，在不同的相中，底层几何结构的不同部分支配着达成一致的时间。最后，我们还考虑了一个话语选民模型，其中选民与他们的邻居讨论他们的意见。我们的证明依赖于众所周知的对偶性来合并随机漫步和对随机图结构的详细理解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Random Structures & Algorithms 数学-计算机：软件工程

CiteScore

2.50

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： It is the aim of this journal to meet two main objectives: to cover the latest research on discrete random structures, and to present applications of such research to problems in combinatorics and computer science. The goal is to provide a natural home for a significant body of current research, and a useful forum for ideas on future studies in randomness. Results concerning random graphs, hypergraphs, matroids, trees, mappings, permutations, matrices, sets and orders, as well as stochastic graph processes and networks are presented with particular emphasis on the use of probabilistic methods in combinatorics as developed by Paul Erdõs. The journal focuses on probabilistic algorithms, average case analysis of deterministic algorithms, and applications of probabilistic methods to cryptography, data structures, searching and sorting. The journal also devotes space to such areas of probability theory as percolation, random walks and combinatorial aspects of probability.