AI 中文总结
研究点灯人群稳定性率和半径，基于新动力学概念，包括近似不变测度分析及连续塔分解程序，采用描述性组合学和分布式局部算法技术，给出无限生成群稳定性半径明确多项式界。
AI 中文摘要
我们建立了点灯人群稳定性率和半径的明确多项式界。这为具有稳定性半径明确上界的无限生成群提供了首个例子，回答了第一作者、列维特和维格多罗维奇的一个问题。我们的方法基于新的动力学概念，包括对近似不变测度的分析。我们为存在周期点的近似不变测度建立了有效的连续塔分解程序。为获得多项式界，我们采用了描述性组合学和分布式局部算法的最新技术。
英文摘要
We establish explicit polynomial bounds on the stability rate and radius of the lamplighter group. This provides the first example of an infinitely presented group with an explicit upper bound on the stability radius, answering a question of the first author, Levit and Vigdorovich. Our approach is based on new dynamical notions, including the analysis of approximately invariant measures. We establish an effective continuous tower decomposition procedure for approximately invariant measures with presence of periodic points. To achieve polynomial bounds we appeal to recent techniques from descriptive combinatorics and distributed LOCAL algorithms.
Comments34 pages
