Commutative Monoid Duality

Jan Niklas Latz () and Jan M. Swart ()
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Jan Niklas Latz: The Czech Academy of Sciences, Institute of Information Theory and Automation
Jan M. Swart: The Czech Academy of Sciences, Institute of Information Theory and Automation

Journal of Theoretical Probability, 2023, vol. 36, issue 2, 1088-1115

Abstract: 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.

Keywords: Interacting particle system; Duality; Monoid; Semiring; Primary: 82C22; Secondary: 16Y60; 20M32 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10959-022-01197-7

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