A model of consensus leads to examples in which the ergodic behavior of a nonstationary product of random nonnegative matrices depends discontinuously on a continuous parameter. In these examples, a product of random matrices, each of which is a scrambling stochastic matrix, changes from being weakly ergodic (asymptotically of rank 1) with probability 1 to being weakly ergodic with probability 0 as a parameter of the process changes smoothly. © 1986.
Cohen, J. E., Hajnal, J., & Newman, C. M. (1986). Approaching consensus can be delicate when positions harden. Stochastic Processes and Their Applications, 22(2), 315–322. https://doi.org/10.1016/0304-4149(86)90008-6