A Constructive Approach to $q$-Gaussian Distributions: $\hat{I}\pm$-Divergence as Rate Function and Generalized de Moivre-Laplace Theorem

Hiroki Suyari, Antonio M. Scarfone

The Large Deviation Principle (LDP) and the Central Limit Theorem (CLT) are central pillars of probability theory. While their formulations are established under the i.i.d. assumpt…