Networks of reinforced stochastic processes: probability of asymptotic polarization and related general results
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910996654718976 |
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| author | Aletti, Giacomo Crimaldi, Irene Ghiglietti, Andrea |
| author_facet | Aletti, Giacomo Crimaldi, Irene Ghiglietti, Andrea |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07687 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Networks of reinforced stochastic processes: probability of asymptotic polarization and related general results Aletti, Giacomo Crimaldi, Irene Ghiglietti, Andrea Probability Statistics Theory Methodology 60F15, 60K35, 91D30 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. |
| title | Networks of reinforced stochastic processes: probability of asymptotic polarization and related general results |
| topic | Probability Statistics Theory Methodology 60F15, 60K35, 91D30 |
| url | https://arxiv.org/abs/2212.07687 |