A concentration inequality for product spaces

TL;DR

This paper establishes a concentration inequality demonstrating that, under mild conditions, variables on large product spaces behave pseudorandomly, highlighting their regularity and predictability.

Contribution

It introduces a new concentration inequality applicable to variables on product spaces, expanding understanding of their pseudorandom behavior.

Findings

Variables on large product spaces exhibit pseudorandom behavior.

The inequality applies under mild regularity conditions.

Provides a tool for analyzing high-dimensional probabilistic systems.

Abstract

We prove a concentration inequality which asserts that, under some mild regularity conditions, every random variable defined on the product of sufficiently many probability spaces exhibits pseudorandom behavior.