Diffusive clustering in an infinite system of hierarchically interacting diffusions.
- Fleischmann, Klaus
- Greven, Andreas
2010 Mathematics Subject Classification
- 60K35 60J60 60J15
- Interacting diffusions, coalescing random walk, hierachial system, cluster formation, universality
We study a countable system of interacting diffusions on the interval [0,1], indexed by a hierarchical group. A particular choice of the interaction guarantees, we are in the diffusive clustering regime. This means clusters of components with values either close to 0 or close to 1 grow on various different scales. However, single components oscillate infinitely often between values close to 0 and close to 1 in such a way that they spend fraction one of their time together and close to the boundary. The processes in the whole class considered and starting with a shift-ergodic initial law have the same qualitative properties (universality).
- Probab. Theor. Relat. Fields, 98 (1994), pp. 517--566