Abstract:

Hall, Deckert and Wiseman (2014) proposed that quantum mechanics can be understood as the continuum limit of a deterministic theory in which quantum effects arise solely from the interaction of finitely many classical “worlds.”  A Gaussian limit for particle positions in the ground state of a harmonic oscillator, agreeing with classical quantum theory, was conjectured by these authors, and proved by McKeague and Levin (2016, Annals of Applied Probability).   In this talk I discuss how corresponding limits for higher energy states can be obtained using Stein's Method.  The talk is based on joint work with Erol Pekoz and Yvik Swan (arXiv:1606.06618, to appear in Bernoulli).