This work initially grew out of investigations on ligand transport
inside proteins. It entails the description of molecular transport in protein
matter and cellular compartments by minmalist random walk models. Interestingly,
the same class of models can be used to describe macrostate fluctuations
due to microscopic conformationial dynamics, like the open-close fluctuations
of ion channel proteins. An additional topic is the effective description
of observables of these random walks, using the generalized moment expansion
and the strong collision approximation of the diffusion operator. Recent
results are on the asymptotic behavior of random walks on random partitionings,
with applications to ion channel fluctuations, and on a systematic extension
of the strong collision approximation and its application to spin dephasing,
with interesting applications to the NMR analysis of biological tissues.
Current investigations deal with models for facilitated transport.
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