Inversion of Characteristic Functions Without Imaginary Unit
Abstract
We start from a pure vector update of the concepts of complex number and characteristic function of a probability distribution, free from the imaginary unit, and reprove some basic properties of the latter. In particular, we derive vector inverse formulas for probability distributions and density functions, provide a new geometric proof of the convergence of suitably centered and normalized vector powers of characteristic functions, and thus provide an update to the proof of the central limit theorem.
Fields of Study & Subjects
Random Matrices and Applications
Statistical Mechanics and Entropy
Mathematical Inequalities and Applications
Publication details
- Journal / source
- Preprints.org
- Publisher
- MDPI AG
- Publication date
- 27 January 2026
- Document type
- Preprint