论文标题
浆果式的平滑不平等，用于紧凑型谎言组的瓦斯坦斯坦公制
Berry-Esseen smoothing inequality for the Wasserstein metric on compact Lie groups
论文作者
论文摘要
我们证明了急剧的一般不平等，估计了沃斯斯坦公制中紧凑型谎言组的两种概率度量的距离，从其傅立叶变换来看。我们使用了瓦斯恒星度量的广义形式，由坎托罗维奇二元性与任意处方的连续性模量有关。证明是基于合适的内核平滑的，以及连续功能的傅立叶衰减估计值。作为推论，我们表明，即使不假定光谱差距，在瓦斯恒星度量中，在瓦斯坦斯坦公制中的半神经群上随机步行的收敛速度几乎是指数呈指数呈指数呈指数呈指数呈指数的。还提供了等距和经验措施的应用。
We prove a sharp general inequality estimating the distance of two probability measures on a compact Lie group in the Wasserstein metric in terms of their Fourier transforms. We use a generalized form of the Wasserstein metric, related by Kantorovich duality to the family of functions with an arbitrarily prescribed modulus of continuity. The proof is based on smoothing with a suitable kernel, and a Fourier decay estimate for continuous functions. As a corollary, we show that the rate of convergence of random walks on semisimple groups in the Wasserstein metric is necessarily almost exponential, even without assuming a spectral gap. Applications to equidistribution and empirical measures are also given.
