Networks of reinforced stochastic processes: probability of asymptotic polarization and related general results
arXiv:2212.07687 · doi:10.1016/j.spa.2024.104376
Abstract
In a network of reinforced stochastic processes, for certain values of the parameters, all the agents' inclinations synchronize and converge almost surely toward a certain random variable. The present work aims at clarifying when the agents can asymptotically polarize, i.e. when the common limit inclination can take the extreme values, 0 or 1, with probability zero, strictly positive, or equal to one. Moreover, we present a suitable technique to estimate this probability that, along with the theoretical results, has been framed in the more general setting of a class of martingales taking values in [0, 1] and following a specific dynamics.
second part of arXiv:2206.07514, 22 pages (appendix 3 pages), 2 figures