Open Access
2023 Applying monoid duality to a double contact process
Jan Niklas Latz, Jan M. Swart
Author Affiliations +
Electron. J. Probab. 28: 1-26 (2023). DOI: 10.1214/23-EJP961


In this paper we use duality techniques to study a coupling of the well-known contact process (CP) and the annihilating branching process. As the latter can be seen as a cancellative version of the contact process, we rebrand it as the cancellative contact process (cCP). Our process of interest will consist of two components, the first being a CP and the second being a cCP. We call this process the double contact process (2CP) and prove that it has (depending on the model parameters) at most one invariant law under which ones are present in both processes. In particular, we can choose the model parameters in such a way that CP and cCP are monotonely coupled. In this case also the above mentioned invariant law will have the property that, under it, ones (modeling “infected individuals”) can only be present in the cCP at sites where there are also ones in the CP. Along the way we extend the dualities for Markov processes discovered in our paper “Commutative monoid duality” to processes on infinite state spaces so that they, in particular, can be used for interacting particle systems.

Funding Statement

Work supported by grant 20-08468S of the Czech Science Foundation (GAČR) and by the grant SVV No. 260701.


We would like to thank the referees for their thorough reading of the manuscript and the helpful suggestions they made.


Download Citation

Jan Niklas Latz. Jan M. Swart. "Applying monoid duality to a double contact process." Electron. J. Probab. 28 1 - 26, 2023.


Received: 14 September 2022; Accepted: 13 May 2023; Published: 2023
First available in Project Euclid: 29 May 2023

MathSciNet: MR4594798
zbMATH: 07721258
Digital Object Identifier: 10.1214/23-EJP961

Primary: 82C22
Secondary: 20M32 , 60K35

Keywords: annihilating branching process , cancellative contact process , contact process , Duality , Interacting particle system , monoid

Vol.28 • 2023
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