Optimal Bounds in Normal Approximation for Many Interacting Worlds
Abstract
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. (2014)]. Our bounds on the Wasserstein distance solve a conjecture of McKeague and Levin [Ann. Appl. Probab. (2016)].
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