Random processes of the form X(n+1) = AnXn + Bn (mod p) in two dimensions
Bianco, Scott Christopher · Scholars Archive - University at Albany (University at Albany, State University of New York) · 2012
A common way for computers to generate pseudo random number sequences is by using recurrences such as Xn+1=aXn+b (mod p) where a, b, and p are fixed integers. Even though this process generates pseudo random numbers it is completely determined by X0,a,b,p. Chung, Diaconis, and Graham, found bounds as p → infinity for the random process Xn+1=aXn+bn (mod p) where a is a fixed integer, and bn is either -1,0, or 1.