On a bound of Hoeffding in the complex case

TL;DR

This paper extends Hoeffding's inequality, originally for real variables, to the complex domain, providing a new bound for complex random variables.

Contribution

The paper generalizes Hoeffding's inequality from real to complex random variables, filling a gap in probabilistic bounds for complex-valued data.

Findings

Derived a Hoeffding-type bound for complex random variables

Established the inequality for variables confined to a bounded complex domain

Provides theoretical foundation for probabilistic analysis of complex data

Abstract

It was proved by Hoeffding in 1963 that a real random variable X confined to [a, b] satisfies E e^(X--E X) $\le$ e^((b--a)^2/8). We generalise this to complex random variables.