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

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  • Aletti, Giacomo
  • Crimaldi, Irene
  • Ghiglietti, Andrea

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.

Suggested Citation

  • Aletti, Giacomo & Crimaldi, Irene & Ghiglietti, Andrea, 2024. "Networks of reinforced stochastic processes: Probability of asymptotic polarization and related general results," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:spapps:v:174:y:2024:i:c:s0304414924000826
    DOI: 10.1016/j.spa.2024.104376
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    References listed on IDEAS

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    1. Crimaldi, Irene & Dai Pra, Paolo & Louis, Pierre-Yves & Minelli, Ida G., 2019. "Synchronization and functional central limit theorems for interacting reinforced random walks," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 70-101.
    2. Aletti, Giacomo & Ghiglietti, Andrea, 2017. "Interacting generalized Friedman’s urn systems," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2650-2678.
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