  We present a convergence result for infinite products of stochastic matrices
with positive diagonals. We regard infinity of the product to the left. Such a
product converges partly to a fixed matrix if the minimal positive entry of
each matrix does not converge too fast to zero and if either zero-entries are
symmetric in each matrix or the length of subproducts which reach the maximal
achievable connectivity is bounded.
  Variations of this result have been achieved independently in Lorenz 2005,
Moreau 2005 and Hendrickx 2005. We present briefly the opinion dynamics
context, discuss the relations to infinite products where infinity is to the
right (inhomogeneous Markov processes) and present a small improvement and
sketch another.
