The dynamics of doubly stochastic operators on finite dimensional simplex

Abstract

We define a doubly stochastic operator on a finite dimensional simplex and study the limit behavior of the trajectories under doubly stochastic operators. We prove that except for certain points, the trajectory of a point, under the doubly stochastic operator, tends to the center of the simplex.

This paper has been withdrawn by the author since the counter-example is contained in the book: A. Marshall, I. Olkin, B. Arnold, Inequaliies: Theory of Majorization and its applications, 2nd Ed. Springer,2011. Page 72 example I.5