Deterministic Versus Stochastic Consensus Dynamics on Graphs

Dylan Weber, Ryan Theisen, Sebastien Motsch

Research output: Contribution to journalArticle

2 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)
JournalJournal of Statistical Physics
StatePublished - Jan 1 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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