论文标题
部分可观测时空混沌系统的无模型预测
Stability estimates for the sharp spectral gap bound under a curvature-dimension condition
论文作者
论文摘要
我们研究了满足曲率结合的度量度量空间的尖锐光谱间隙边界的稳定性。即使在平滑环境中，我们的主要结果是一个急剧的定量估计值，表明，如果RCD $（N-1，N）$空间的光谱差距几乎是最小的，那么与光谱差距相关的特征功能的量度接近Beta分布。该证明结合了对使用Stein的分布近似方法的RCD空间的新的$ l^1 $功能不平等获得的本本函数的估计。我们还得出了对维度参数的无限和负值的类似，几乎清晰的估计。
We study stability of the sharp spectral gap bounds for metric-measure spaces satisfying a curvature bound. Our main result, new even in the smooth setting, is a sharp quantitative estimate showing that if the spectral gap of an RCD$(N-1, N)$ space is almost minimal, then the pushforward of the measure by an eigenfunction associated with the spectral gap is close to a Beta distribution. The proof combines estimates on the eigenfunction obtained via a new $L^1$-functional inequality for RCD spaces with Stein's method for distribution approximation. We also derive analogous, almost sharp, estimates for infinite and negative values of the dimension parameter.
