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\end{enumerate}  I'm sure there are many tools from Matthieu's class which would come in useful.  Thoughts:   \underline{Question 1:}  A first step is to solve the (coupled) diffusion equations of the medium and (mean field?). This gives coarse, deterministic behaviour. Then need a way into the statistics. Read Matthieu's notes. Can we use RG (see Bertin 2009, Matthieu)?