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 and following a specific dynamics.

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

Crimaldi Irene;
In corso di stampa

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 and following a specific dynamics.
In corso di stampa
Interacting random systems Network-based dynamics Reinforced stochastic processes Urn models Martingales Polarization Touching the barriers Opinion dynamics Simulations
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11771/28618
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