  We present a results about convergence of products of row-stochastic matrices
which are infinite to the left and all have positive diagonals. This is
regarded as in inhomogeneous consensus process where confidence weights may
change in every time step but where each agent has a little bit of self
confidence. The positive diagonal leads to a fixed zero pattern in certain
subproducts of the infinite product.
  We discuss the use of the joint spectral radius on the set of the evolving
subproducts and conditions on the subprodutcs to ensure convergence of parts of
the infinite product to fixed rank-1-matrices on the diagonal.
  If the positive minimum of each matrix is uniformly bounded from below the
boundedness of the length of intercommunication intervals is important to
ensure convergence. We present a small improvement. A slow increase as quick as
log(log(t)) in the length of intercommunication intervals is acceptable.
