Abstrakt
In the study of interacting particle systems (IPS) duality is an important tool used to prove, for example, convergence to an invariant distribution or the existence of clusters. While the two most used types of dualities are additive and cancellative dualities [1], Lloyd and Subdury [2, 3, 4], have defined more general duality functions, that are able "interpolate" between additive and cancellative dualities.
To gain a better understanding why this approach is very successful in practice, we leave the well-known case of IPS taking values in {0,1}^Λ, where Λ is some lattice, and generalise the ideas of Lloyd and Sudbury to IPS taking values in {0,1,...,n-1}^Λ for general n >= 2. In this talk I will focus on the case n = 3, discuss strategies how to define promising duality functions and test them on the voter model as an example.