Majority dynamics on random graphs: The multiple states case

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2025-05-27 DOI:10.1016/j.spa.2025.104682

Jordan Chellig, Nikolaos Fountoulakis

引用次数: 0

Abstract

We study the evolution of majority dynamics with more than two states on the binomial random graph

G (n, p)

. In this process, each vertex has a state in

{1, \dots, k}

, with

k \geq 3

, and at each round every vertex adopts state

i

if it has more neighbours in state

i

than in any other state. Ties are resolved randomly. We show that with high probability the process reaches unanimity in at most three rounds, if

n p ≫ n^{2 / 3}

查看原文本刊更多论文

随机图上的多数动态：多状态情况

研究了二项随机图G（n,p）上具有两个以上状态的多数动力学的演化。在这个过程中，每个顶点都有一个状态{1，…，k}，且k≥3，在每一轮中，如果处于状态i的邻居比处于其他状态的邻居多，则每个顶点都采用状态i。平局是随机解决的。我们证明了在np = n2/3的条件下，该过程有高概率在最多三轮内达到一致。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.