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A stochastic model of discussion

Author

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  • Plaszczynski, S.
  • Grammaticos, B.
  • Badoual, M.

Abstract

We consider the duration of discussions in face-to-face contacts and propose a stochastic model to describe it. It is based on the points of a Levy flight where the duration of each contact corresponds to the size of the clusters produced during the walk. When confronting it to the data measured from proximity sensors, we show that several datasets obtained in different environments, are precisely reproduced by the model fixing a single parameter, the Levy index, to 1.15. We analyze the dynamics of the cluster formation during the walk and compute analytically the cluster size distribution. We find that discussions are first driven by a maximum-entropy geometric distribution and then by a rich-get-richer mechanism reminiscent of preferential-attachment (the more a discussion lasts, the more it is likely to continue). In this model, conversations may be viewed as an aggregation process with a characteristic scale fixed by the mean interaction time between the two individuals.

Suggested Citation

  • Plaszczynski, S. & Grammaticos, B. & Badoual, M., 2024. "A stochastic model of discussion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 652(C).
    • Handle: RePEc:eee:phsmap:v:652:y:2024:i:c:s0378437124005570
    DOI: 10.1016/j.physa.2024.130048
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    References listed on IDEAS

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    1. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    2. Petter Holme, 2015. "Modern temporal network theory: a colloquium," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(9), pages 1-30, September.
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