OPTIMAL BOUNDS IN NORMAL APPROXIMATION FOR MANY INTERACTING WORLDS

• 成果类型: Article
• 署名作者: Chen, Louis H. Y.; Thanh, Le Van
• 署名单位: National University of Singapore; Vinh University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/21-AAP1747
• 发表日期: 2023
• 页码: 625-642
• 关键词: suggested interpretation; quantum-theory; steins method; terms

摘要

In this paper, we use Stein's method to obtain optimal bounds, both in Kolmogorov and in Wasserstein distance, in the normal approximation for the empirical distribution of the ground state of a many-interacting-worlds harmonic oscillator proposed by Hall, Deckert and Wiseman (Phys. Rev. X 4 (2014) 041013). Our bounds on the Wasserstein distance solve a conjecture of McKeague and Levin (Ann. Appl. Probab. 26 (2016) 2540-2555).