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Humboldt-Universität zu Berlin - Faculty of Mathematics and Natural Sciences - RTG1845

 

Stochastic processes in physics and biology

 

 

The research in this field centers around interacting stochastic processes describing complex systems arising in the natural sciences, in particular in the rapidly developing field of mathematical biology (including the new focus stochastic processes in neuroscience) and in the well-established yet highly fruitful field of statistical physics. Our main goal is the rigorous mathematical understanding of the macroscopic resp. long-term behavior of interacting systems that are described by a set of microscopic probabilistic rules with many degrees of freedom. Typical phenomena occurring in this context are phase transitions, universality of scaling limits and genealogies, emergence of coexistence and extinction regimes, Gibbsian structures, intermittency or synchronization of weakly coupled oscillators. The faculty members with a focus of activity in this domain are J. Blath, J.-D. Deuschel, W. König, N. Kurt, S. Rœlly and W. Stannat.

 

Main research fields

 

Mathematical biology

 

  • Stochastic models in genetics,
  • Spatial stochastic population dynamics,
  • Multitype branching populations near extinction,
  • Noise in neural systems.

 

Statistical physics

 

  • The parabolic Anderson model and the randomized Laplace operator,
  • Symmetric random walks and diffusions in random environment,
  • Phase transitions for particle systems with Lennard-Jones potential,
  • Strongly interactive diffusions and Gibbs measures.