We consider finite-state time-nonhomogeneous Markov chains whose transition matrix at time n is I+G/n<SUP><FONT FACE="Symbol">z</FONT></SUP> where G is a ``generator'' matrix, that is G(i,j)0 for i,j distinct, and G(i,i)= -∑<SUB>k<FONT FACE="Symbol">≠</FONT>i</SUB> G(i,k), and <FONT FACE="Symbol">z</FONT>0 is a strength parameter. In these chains, as time grows, the positions are less and...</font></font></sub></font></sup>