Optimal Bounds in Normal Approximation for Many Interacting Worlds

In this paper, we use Stein's method to obtain optimal bounds, both Kolmogorov and Wasserstein, 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)].