Doron Gepner's Statistics on Words in {1,2,3} is (most probably) Asymptotically Logistic

TL;DR

This paper investigates Doron Gepner's word statistics from conformal field theory, providing evidence that its scaled limiting distribution converges to the Logistic distribution, contrasting with the normal distribution of similar classical statistics.

Contribution

The paper rigorously proves the convergence of the first twelve moments of Gepner's statistics to those of the Logistic distribution, suggesting asymptotic logistic behavior.

Findings

Scaled moments of Gepner's statistics converge to Logistic distribution moments

Gepner's statistics differ from classical inversion statistics which are asymptotically normal

Supports conjecture of logistic limiting distribution through moment analysis

Abstract

Doron Gepner's word statistics, that came up in his research in conformal field theory, is studied and it is conjectured that its scaled limiting distribution is the Logistic distribution. We support this by proving rigorously that the scaled limits of the first twelve moments do indeed converge to those of the Logistic distribution. This is surprising, since Gepner's statistics is a natural analog of the classical statistics called the number of inversion, that is known to be asymptotically normal.