Journal of Statistical Physics

, Volume 176, Issue 1, pp 40–68 | Cite as

Deterministic Versus Stochastic Consensus Dynamics on Graphs

  • Dylan WeberEmail author
  • Ryan Theisen
  • Sebastien Motsch


We study two agent based models of opinion formation—one stochastic in nature and one deterministic. Both models are defined in terms of an underlying graph; we study how the structure of the graph affects the long time behavior of the models in all possible cases of graph topology. We are especially interested in the emergence of a consensus among the agents and provide a condition on the graph that is necessary and sufficient for convergence to a consensus in both models. This investigation reveals several contrasts between the models—notably the convergence rates—which are explored through analytical arguments and several numerical experiments.


Dynamical systems Agent based modeling Stochastic modeling Deterministic modeling Network dynamics Consensus dynamics 



This work has been supported by the NSF Grants DMS-1515592 and RNMS11-07444 (KI-Net).


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Authors and Affiliations

  1. 1.School of Mathematics and Statistical SciencesArizona State UniversityTempeUSA
  2. 2.Department of StatisticsUniversity of California, BerkeleyBerkeleyUSA

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