Abstrakt
A theory of dual processes for attractive spin systems was developed by Gray in 1986. In 2018, based on Gray's work, Sturm and Swart systematically investigated monotonicity-based pathwise dualities for Markov processes in general and interacting particle systems in particular.
However, the authors only prove the well-definedness of the dual process if started from finite initial states. This talk indicates how to construct a well-defined pathwise dual process of a monotone interacting particle system that can also be started from an infinite initial state.
This then allows us to study invariant laws of the dual process and connect them to properties of the original interacting particle system.