Some Gaussianity criteria for Khinchin families

TL;DR

This paper develops straightforward analytical conditions to determine when a Khinchin family, associated with a power series, exhibits Gaussian behavior, supported by moment criteria and various applications.

Contribution

It introduces new verifiable criteria for Gaussianity in Khinchin families, expanding understanding of their probabilistic properties.

Findings

Established simple analytical conditions for Gaussianity.

Provided moment-based criteria applicable to non-negative coefficient series.

Demonstrated applications of these criteria in various contexts.

Abstract

In this note we establish simple and verifiable analytical conditions for a power series f in the class K, and its associated Khinchin family, to be Gaussian. We give several moment criteria for general power series with non-negative coefficients in K and also provide several applications of these criteria.