Poisson actions of noncompact locally compact sofic groups have completely positive sofic entropy

Abstract

We prove that every Poisson action of positive intensity of a noncompact locally compact second countable sofic group has completely positive measure sofic entropy with respect to every locally compact sofic approximation. The proof constructs random microstates for arbitrary measurable factors by completing local Poisson configurations with an independent exterior Poisson process. Probability estimates and a packing argument then show that every nontrivial factor has positive entropy. We also give a compact-group example showing that the noncompactness assumption is essential.