Inverting the central limit theorem

Details Inverting the central limit theorem Inverting the central limit theorem

2011-10-11

arxiv.org/abs/1110.2394v2

Physics

Quantum Physics

Proof of strong NP-hardness. Connection with random walks. New asymptotic results. Numerous typos corrected

Scientific paper

The central limit theorem states that the sum of N independently distributed n-tuples of real variables (subject to appropriate normalization) tends to a multivariate gaussian distribution for large N. Here we propose to invert this argument: given a set of n correlated gaussian variables, we try to infer information about the spectrum of the discrete microscopic probability distributions whose convolution generated such a macroscopic behavior. The techniques developed along the article are applied to prove that the classical description of certain macroscopic optical experiments is infinitely more complex than the quantum one.

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