Synthetic Data and Generative AI

Chapter 12: Some unusual random walks

Testing and leveraging quasirandomness

Abstract

This is a follow-up to Chapter 11 about “Detecting Subtle Departures from Randomness”, where I introduced the prime test to identify very weak violations of various laws of large numbers. Pseudorandom sequences failing this test usually pass most test batteries, yet are unsuitable for a number of applications, such as security, strong cryptography, or intensive simulations. The purpose here is to build such sequences with very low, slow-building, long-range dependencies, but that otherwise appear as random as pure noise. They are useful not only for testing and benchmarking tests of randomness, but also in their own right to model almost random systems, such as ...