Random walks on randomly partitioned lattices with applications toward protein fluctuations

Random walks on state space partitions provide an abstract generic picture for the description of macroscopic fluctuations in complex systems like proteins. We first determine the average residence probability and the average distribution of residence times in a particular macroscopic state for the ensemble of random partitions of a one-dimensional state space.;We then extend our study to the Bethe lattice and also the 2-, 3- and higher dimensional lattices. Our treatment involves both extensive analytical and numerical analyses. Finally, we compare the solution of our model on the Bethe lattice with the experimental data and find excellent agreement.