Stochastic interacting particle systems in statistical physics and biology

The second major theme of the research program centers around the notion of microscopic stochastic modeling of complex systems. The main paradigm here is the notion of static and dynamic systems of particles subject to random forces or stochastic dynamics involving mutual interactions, respectively interactions with a (random) environment. Such models are typically motivated from statistical physics and mathematical biology. One is interested in understanding phenomena occurring on a macroscopic scale which emerge due to the microscopic interactions of the system. Important examples are phase transitions, emergence of scaling limits, long-time asymptotic behavior and ageing. Specific models in which such behavior can be studied are

  • random walks in random environment,
  • interface models,
  • interacting diffusions,
  • spin glasses,
  • percolation on general graphs,
  • branching processes and branching particle systems,
  • stochastic population dynamics,
  • parabolic Anderson model,
  • random polymers,
  • random matrices.