多项式体积增长群上类稳定随机游动的狄利克雷形式比较
Comparison of Dirichlet forms for stable-like random walks on groups of polynomial volume growth
浏览论文内容
中文总结 AI 辅助
本研究针对多项式体积增长群上由特定测度驱动的类稳定随机游动，建立了其关联狄利克雷形式等价性的几何与代数判定准则，用于比较两类随机游动的行为。
中文摘要 AI 辅助
在前期工作中，我们研究了有限生成幂零群乃至更一般的多项式体积增长群上类稳定随机游动的自然实例，这类游动由径向型、坐标型或这类测度的凸组合驱动。本工作中，我们探究此类随机游动何时具有可比行为，衡量标准是其关联狄利克雷形式的等价性，并从驱动测度与群的几何及代数特征出发，建立了该等价性的判定准则。
英文摘要
In earlier works, we studied natural examples of stable-like random walks on finitely generated nilpotent groups and, more generally, on groups of polynomial volume growth. These walks are driven by measures of radial type, coordinate-wise type, or convex combinations of such measures. In the present work, we explore when two such random walks have comparable behavior, as measured by the equivalence of their associated Dirichlet forms. We develop criteria for this equivalence in terms of both geometric and algebraic features of the driving measures and the group.
