A refined central limit theorem for spin systems with applications

I will explain the way in which the central limit theorem (CLT), a well known statement in probability theory, appears as a universal feature of the wave-functions of plenty of states of many-body quantum systems. I will also introduce and give a proof sketch of the Berry-Esseen theorem in this context, which provides a quantitative strengthening of the CLT. If time allows, I will also sketch how these ideas allows us to prove some rigorous results about non-equilibrium dynamics, and about the performance of certain quantum and classical algorithms for thermal expectation values.

https://arxiv.org/abs/2307.05200