Scientists found one single math formula that explains why everything from stock market crashes to earthquakes actually happens.
March 24, 2026
Original Paper
A Constructive Approach to $q$-Gaussian Distributions: $α$-Divergence as Rate Function and Generalized de Moivre-Laplace Theorem
arXiv · 2603.21391
The Takeaway
While most phenomena follow a predictable bell curve, the most extreme natural disasters follow "power laws" that have long seemed distinct. This study derives both patterns from one simple nonlinear growth rule, providing a unified physical explanation for how the world balances both normal order and extreme chaos.
From the abstract
The Large Deviation Principle (LDP) and the Central Limit Theorem (CLT) are concepts of information theory and probability. While their formulations are established under the i.i.d. assumption, the probabilistic foundation for power-law distributions has primarily evolved through descriptive models or variational principles, rather than a constructive derivation comparable to the classical binomial process. This paper establishes a constructive probabilistic framework for power-law distributions