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Commutative Monoid Duality

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jan Niklas Latz & Jan M. Swart, 2023. "Commutative Monoid Duality," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1088-1115, June.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:2:d:10.1007_s10959-022-01197-7
    DOI: 10.1007/s10959-022-01197-7
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    References listed on IDEAS

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    1. Carinci, Gioia & Giardinà, Cristian & Giberti, Claudio & Redig, Frank, 2015. "Dualities in population genetics: A fresh look with new dualities," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 941-969.
    2. Aidan Sudbury, 2000. "Dual Families of Interacting Particle Systems on Graphs," Journal of Theoretical Probability, Springer, vol. 13(3), pages 695-716, July.
    3. Anja Sturm & Jan M. Swart, 2018. "Pathwise Duals of Monotone and Additive Markov Processes," Journal of Theoretical Probability, Springer, vol. 31(2), pages 932-983, June.
    4. Bramson, Maury & Wan-ding, Ding & Durrett, Rick, 1991. "Annihilating branching processes," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 1-17, February.
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