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In a network of reinforced stochastic processes, for certain values of theparameters, all the agents' inclinations synchronize and converge almost surelytoward a certain random variable. The present work aims at clarifying when theagents can asymptotically polarize, i.e. when the common limit inclination cantake the extreme values, 0 or 1, with probability zero, strictly positive, orequal to one. Moreover, we present a suitable technique to estimate thisprobability that, along with the theoretical results, has been framed in themore general setting of a class of martingales taking values in [0, 1] andfollowing a specific dynamics.

Networks of reinforced stochastic processes: probability of asymptotic polarization and related general results