5 papers · 1 filter
Poisson actions of noncompact locally compact sofic groups have completely positive sofic entropy
Zhuowei Liu
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…
A Hard-Core Subshift Whose Sofic Mean Dimension Depends on the Sofic Approximation
Xianqiang Li, Zhuowei Liu
We exhibit a topologically mixing continuous-alphabet subshift of the free group whose sofic mean dimension depends on the chosen homomorphic sofic approximation, which gives…
Equivalence of Sofic -Metric Mean Dimensions and a Tame-Metric Variational Formula
Xianqiang Li, Zhuowei Liu
Let be a countable discrete sofic group acting by homeomorphisms on a compact metrizable space and a sofic approximation of . We prove that for every $1\leq p<\infty…
Relative entropy, topological pressure and variational principle for locally compact sofic group actions
Xianqiang Li, Zhuowei Liu
For a locally compact sofic group continuously acting on a compact metric space, we first study the relative sofic entropy and prove an additive inequality relating sofic entropy a…
Sofic conditional mean dimension, relative sofic mean dimension and their localizations
Xianqiang Li, Zhuowei Liu, Xiaofang Luo
Let be a factor map between continuous actions of a sofic group , we study sofic conditional mean dimension and relative sofic mean dimension introduced in \…