Random cyclic transformations of points
J. G. Veitch, G. S. Watson · Journal of Applied Probability · 1986
We consider the action of independent and identically distributed n × n circulants S 1, S 2, … on V = [v 1, …, vn ] whose columns are the positions of n points in ℝ d . The positions of the n points after m transformations are the columns of W (m) = VS 1 … Sm . We describe, in several ways, the shape of the configuration of the points W (m) as m →∞. When n = 3, 4 and d = 2, a special discussion in terms of Moebius transformations is given.