Random walks on random partitions in one dimension.

Random walks on state space partitions provide an abstract generic picture for the description of macroscopic uctuations in heterogeneous systems like proteins. We 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. In particular, the probability that a walker remains in an open-state cluster decays in a manner that is slower than exponential, but faster than a power law.