A Model for Random Random-Walks on Finite Groups

Source abstract

A model for a random random-walk on a finite group is developed where the group elements that generate the random-walk are chosen uniformly and with replacement from the group. When the group is the d-cube Z d 2 , it is shown that if the generating set is size k then as d → ∞ with k − d → ∞ almost all of the random-walks converge to uniform in k ln ( k /( k − d ))/4+ρ k steps, where ρ is any constant satisfying ρ > −ln (ln 2)/4.