A quantum-mechanical derivation of the multivariate central limit theorem for Markov chains

Abstract

Abstract The central limit theorem for Markov chains is widely used, in particular in its pristine univariate form. As far as the multivariate case is concerned, a few proofs exist, which depend on different assumptions and require advanced mathematical and statistical tools. Here a novel proof is presented that, starting from the standard condition of regularity only, relies on time-independent quantum-mechanical perturbation theory. The result, which is obtained by using techniques that are typical of physics, is expected to enhance the usability of this cornerstone theorem, especially in nonlinear dynamics and physics of complex systems.