Deterministic Versus Stochastic Consensus Dynamics on Graphs

Dylan Weber, Ryan Theisen, Sebastien Motsch

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)40-68
Number of pages29
JournalJournal of Statistical Physics
Issue number1
StatePublished - Jul 15 2019


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

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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