Central limit theorems for correlated variables: some critical remarks

TL;DR

This paper reviews various central limit theorems for correlated variables, discusses potential new versions for specific problems, and questions the special role of q-Gaussians in statistical physics.

Contribution

It provides an elementary review of existing theorems, proposes the possibility of new variants, and critically examines the significance of q-Gaussians in physics.

Findings

Several central limit theorems for correlated variables are discussed.

Potential for new versions of theorems tailored to specific problems.

Insufficient evidence for q-Gaussians' special role in statistical physics.

Abstract

In this talk I first review at an elementary level a selection of central limit theorems, including some lesser known cases, for sums and maxima of uncorrelated and correlated random variables. I recall why several of them appear in physics. Next, I show that there is room for new versions of central limit theorems applicable to specific classes of problems. Finally, I argue that we have insufficient evidence that, as a consequence of such a theorem, q-Gaussians occupy a special place in statistical physics.