Commutative monoid duality
Probability
2022-07-25 v3
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.
Cite
@article{arxiv.2108.01492,
title = {Commutative monoid duality},
author = {Jan Niklas Latz and Jan M. Swart},
journal= {arXiv preprint arXiv:2108.01492},
year = {2022}
}
Comments
26 pages. Renamed some lemmas into propositions, corrected some small errors, minor additions to the discussion