Commutative monoid duality
arXiv:2108.01492
Abstract
We introduce two partially overlapping classes of pathwise dualities between interacting particle systems that are based on commutative monoids (semigroups with a neutral element) and semirings, respectively. For interacting particle systems whose local state space has two elements, this approach yields a unified treatment of the well-known additive and cancellative dualities. For local state spaces with three or more elements, we discover several new dualities.
26 pages. Renamed some lemmas into propositions, corrected some small errors, minor additions to the discussion