Comment on "Towards a large deviation theory for strongly correlated systems"

TL;DR

This paper critically examines a recent claim of a $q$-exponential large deviation principle for correlated systems, demonstrating that the observed scaling results are not unique to the $q$-exponential and can be reproduced with simpler models.

Contribution

The paper shows that the numerical scaling results attributed to a $q$-exponential generalization are not exclusive to correlated systems and can be derived from independent variables or other power-law deformations.

Findings

Scaling results are reproducible with independent variables.

Results are not uniquely linked to the $q$-exponential function.

The claimed generalization lacks conclusive support.

Abstract

I comment on a recent paper by Ruiz and Tsallis [Phys. Lett. A 376, 2451 (2012)] claiming to have found a '$q$-exponential' generalization of the large deviation principle for strongly correlated random variables. I show that the basic scaling results that they find numerically can be reproduced with a simple example involving independent random variables, and are not specifically related to the $q$-exponential function. In fact, identical scaling results can be obtained with any other power-law deformations of the exponential. Thus their results do not conclusively support their claim of a $q$-exponential generalization of the large deviation principle.