Monoid duality with a special focus on order-theoretic lattices

Abstract

I present an approach to identify pathwise dualities between interacting particle systems with finite local state spaces via commutative monoids (i.e. semigroups containing a neutral element). This approach reveals formerly unknown dualities on local state spaces with more than two elements and, moreover, it allows us to treat several known dualities in a uniform framework.

In particular, additive dualities on lattices can be interpreted as special cases of monoid duality. As an example I will revisit the two-stage contact process discovered by Krone and construct its duality from the perspective of monoid duality.

This is joint work with Jan Swart.