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Zolotarev distances between probability measures are natural analogues of the Kantorovich metric \(W_1\) in which higher-order derivatives of the determining family of functions are considered. This work develops Fourier analytic methods towards the investigation of families of Zolotarev distances on the d-dimensional torus, with applications to rates of convergence of empirical measures, in analogy with the known results for the Kantorovich metrics \(W_p\) , \(p \geq 1\) .

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Fourier Analytic Bounds for Zolotarev Distances and Applications to Empirical Measures

  • 会议论文

  • 发表日期：

    2026年

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  • Sergey G. Bobkov,
  • Michel Ledoux

摘要

Zolotarev distances between probability measures are natural analogues of the Kantorovich metric \(W_1\) in which higher-order derivatives of the determining family of functions are considered. This work develops Fourier analytic methods towards the investigation of families of Zolotarev distances on the d-dimensional torus, with applications to rates of convergence of empirical measures, in analogy with the known results for the Kantorovich metrics \(W_p\) , \(p \geq 1\) .