2018/03/19 by R. L. Hudson · 1 citation
Mathematics · Economics, Econometrics and Finance · Physics and Astronomy · #Random Matrices and Applications #Stochastic processes and financial applications #Quantum Mechanics and Applications
paper · doi:10.1098/rsta.2017.0226
openalex publication_date 2018/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas.This article is part of the themed issue 'Hilbert's sixth problem'.