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

Abstract

In this paper, we use completed root views to study measure sofic entropy of Poisson actions of locally compact sofic groups. We prove that, for every noncompact locally compact second countable sofic group and every locally compact sofic approximation, each positive-intensity Poisson action has completely positive measure sofic entropy. We also compare the averaged and pointwise spatial formulas with Singh's entropy and show that noncompactness is necessary for the theorem as stated.