Revisiting Liggett's theorem on non-interacting particle systems

A classical result due to Liggett characterises all point process which are invariant under non-interacting Markov evolutions. These are exactly Poisson point processes with random intensities. This result has recently come in light due to its applications in extrema Gaussian free field. We will give a new proof of this result. The need of a new proof comes as it avoids the ingredient of the so called Choquet-Deny equation, and hence it can be adapted to the setting of Branching systems (Branching systems will not be discussed in this talk). 
Based on joint work with Christophe Garban and Xinxin Chen. 

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