Anja Sturm
University of Delaware
Title: Interface tightness for long-range voter models with exclusion dynamics.
We prove a theorem on extinction versus unbounded growth for parity preserving cancellative interacting particle systems. Here, extinction or growth refers to the long term behavior of ones ("particles") if the system is started with finitely many ones initially. The theorem is proved under the assumption that the one particle state is not positively recurrent. The result is then applied to parity preserving particle systems in one dimension, which we can interpret as the interface dynamics of mixtures of long-range voter models and exclusion process dynamics. We use this fact to show that the latter models exhibit interface tightness, meaning that the trivial one interface state is positively recurrent, provided that the infection rates have a finite second moment.

This is joint work with Jan Swart (UTIA Prague).

©2008, Department of Mathematical Sciences
Last Modified: September 5, 2008