6 - Duality
Published online by Cambridge University Press: 26 June 2026
Summary
Duality is one of the most basic tools in the study of interacting particle systems. There exist two forms: pathwise and distributional duality, of which the first is the stronger. It is shown how pathwise dualities naturally follow from the basic Poisson construction of Chapter 4 by looking backward in time. The classical additive and cancellative dualities, which are pathwise dualities, are discussed in detail. As an example of dualities that are not pathwise, Lloyd–Sudbury duality is discussed. It is demonstrated how duality can be used to prove various results, such as clustering in the voter model, uniqueness of a homogeneous nontrivial invariant law for the contact process, and equality of the critical points for finite survival and for the existence of a nontrivial invariant law in a contact-voter model.
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- A Course in Interacting Particle Systems , pp. 119 - 152Publisher: Cambridge University PressPrint publication year: 2026
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