Random interacting particle systems

  • Peter Gracar

Student thesis: Doctoral ThesisPhD


Consider the graph induced by Z^d, equipped with uniformly elliptic random conductances on the edges. At time 0, place a Poisson point process of particles on Z^d and let them perform independent simple random walks with jump probabilities proportional to the conductances. It is well known that without conductances (i.e., all conductances equal to 1), an infection started from the origin and transmitted between particles that share a site spreads in all directions with positive speed. We show that a local mixing result holds for random conductance graphs and prove the existence of a special percolation structure called the Lipschitz surface. Using this structure, we show that in the setup of particles on a uniformly elliptic graph, an infection also spreads with positive speed in any direction. We prove the robustness of the framework by extending the result to infection with recovery, where we show positive speed and that the infection survives indefinitely with positive probability.
Date of Award12 Feb 2018
Original languageEnglish
Awarding Institution
  • University of Bath
SupervisorAlexandre De Oliveira Stauffer (Supervisor) & Peter Morters (Supervisor)


  • Percolation
  • Lipschitz
  • Surface
  • Multi-scale

Cite this