On the variational distance of independently repeated experiments

TL;DR

This paper proves that the variational distance between two similar probability distributions' n-fold products grows at most proportionally to the square root of n, providing insights into the behavior of repeated experiments.

Contribution

It establishes an upper bound on the growth rate of variational distance for repeated independent experiments, which was previously unknown.

Findings

Variational distance grows at most as sqrt(n)

Provides bounds for repeated experiment distributions

Enhances understanding of distribution divergence over repetitions

Abstract

Let P and Q be two probability distributions which differ only for values with non-zero probability. We show that the variational distance between the n-fold product distributions P^n and Q^n cannot grow faster than the square root of n.