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Probability and Math Finance Seminar

Anja Sturm, University of Delaware

Survival and coexistence in some cancellative spin systems

Abstract

We consider variations of the usual voter model, which favor types that are locally less common. Such voter models with selection are dual to systems of branching annihilating random walks that are parity preserving. We consider coexistence of types in the voter models which is related to the survival of particles in the branching annihilating random walk. We find conditions for the uniqueness of a homogeneous coexisting invariant law as well as for convergence to this law from homogeneous and coexisting initial laws. For a particular one dimensional model we also show a complete convergence result for any initial condition. This is based on comparison with oriented percolation of the associated branching annihilating random walk.

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

MONDAY, April 14, 2008
Time: 5:00 P.M.
Location: WeH 6423