5 - Monotonicity
Published online by Cambridge University Press: 26 June 2026
Summary
Monotonicity and positive correlations are two basic tools that, when available, greatly facilitate the study of an interacting particle system. After recalling (without proof) the basic properties of the stochastic order, it is shown how one can prove that a given system is monotone or has positive correlations. The lower and upper invariant laws of an interacting particle are introduced and studied, and it is shown how comparison results can be used to show that various functions of an interacting particle system are monotone or to transfer results from one system to another.
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- A Course in Interacting Particle Systems , pp. 104 - 118Publisher: Cambridge University PressPrint publication year: 2026
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