一维Hegselmann-Krause有界置信度动力学收敛速率的二次下界
A quadratic lower bound for the convergence rate in the one-dimensional Hegselmann-Krause bounded confidence dynamics
University of Gothenburg（哥德堡大学）；Chalmers University of Technology（查尔姆斯理工大学）
AI总结：
研究一维Hegselmann-Krause有界置信度动力学中系统达到平衡所需时间步数的下界，证明其为二次增长，匹配k≥2维度的最佳下界。
摘要：
设f_{k}(n)为n个代理遵循k维Hegselmann-Krause有界置信度动力学达到平衡所需的最多时间步数。此前已知Ω(n)=f_{1}(n)=O(n^3)。本文证明f_{1}(n)=Ω(n^2)，这与k≥2所有维度的最佳下界一致。
英文摘要：
Let f_{k}(n) be the maximum number of time steps taken to reach equilibrium by a system of n agents obeying the k-dimensional Hegselmann-Krause bounded confidence dynamics. Previously, it was known that Ω(n) = f_{1}(n) = O(n^3). Here we show that f_{1}(n) = Ω(n^2), which matches the best-known lower bound in all dimensions k >= 2.
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。
