Sharp inequalities between Zolotarev and Wasserstein distances in

• 成果类型: Article; Early Access
• 署名作者: Bolbotowski, Karol; Bouchitte, Guy
• 署名单位: University of Warsaw
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-026-01527-4
• 发表日期: 2026-07-30
• 关键词: Probability metrics; Optimal Transport; Kantorovich-Rubinstein duality; Wasserstein Distance; Zolotarev distance; Rio inequality; MINIMAL DISTANCES

摘要

Based on a new Kantorovich-Rubinstein duality principle for the Hessian that was recently established by the two authors, we extend the Rio inequality to any dimension d >= 1 with an optimal constant. Similarly, we propose an optimal upper bound for the ratio of Zolotarev distance Z2(mu,nu) to Wasserstein distance W2(mu,nu) when mu,nu is an element of P2(Rd) are centred probabilities with prescribed variances.