Universal Attractors of Reversible Aggregate-Reorganization Processes

We analyze a general class of reversible aggregate-reorganization processes. These processes are shown to exhibit globally attracting equilibrium distributions, which are \textit{universal}, i.e. identical for large classes of models. Furthermore, the analysis implies that for studies of equilibrium properties of \textit{any} such process, computationally expensive reorganization dynamics such as random walks can be replaced by more efficient, yet simpler methods. As a particular application, our results explain the recent observation of the formation of similar fractal aggregates from different initial structures by diffusive reorganization [Filoche and Sapoval, Phys. Rev. Lett. 85, 5118 (2000)].