Intermittency on catalysts

Details Intermittency on catalysts Intermittency on catalysts

2007-06-08

arxiv.org/abs/0706.1171v1

Mathematics

Probability

11 pages, invited paper to appear in a Festschrift in honour of Heinrich von Weizs\"acker, on the occasion of his 60th birthda

Scientific paper

The present paper provides an overview of results obtained in four recent papers by the authors. These papers address the problem of intermittency for the Parabolic Anderson Model in a \emph{time-dependent random medium}, describing the evolution of a ``reactant'' in the presence of a ``catalyst''. Three examples of catalysts are considered: (1) independent simple random walks; (2) symmetric exclusion process; (3) symmetric voter model. The focus is on the annealed Lyapunov exponents, i.e., the exponential growth rates of the successive moments of the reactant. It turns out that these exponents exhibit an interesting dependence on the dimension and on the diffusion constant.

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