arXiv subjects

Zhuowei Liu

Publications and source records attributed to Zhuowei Liu.

6 recordsLinked to original sources

arXiv2026

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

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.

math.DS↗

arXiv2026

Equivalence of Sofic $p$-Metric Mean Dimensions and a Tame-Metric Variational Formula

Let $\Gamma$ be a countable discrete sofic group acting by homeomorphisms on a compact metrizable space $X$ and $\Sigma$ a sofic approximation of $\Gamma$. We prove that for every $1\leq p<\infty$, the sofic $p$-metric mean dimension is equivalent to the sofic metric mean dimension, i.e there exists a common value $ D_\Sigma(X,\Gamma)\in\{-\infty\}\cup[0,+\infty]$ such that, $$D_\Sigma(X,\Gamma)=\mdim_{\Sigma,\mathrm M,p}(X,\Gamma) =\mdim_{\Sigma,\mathrm M,\infty}(X,\Gamma),$$ which answers a question of Hayes in \cite[Question 3]{Hayes}. Moreover, a tame-metric variational formula is established. That is for every $1\leq q\leq\infty$, $$D_\Sigma(X,\Gamma) =\inf_{\rho\in\mathcal T(X)} \underline{\mdim}_{\Sigma,q}(X,\rho), $$ where $\mathcal T(X)$ is the set of all compatible metrics on $X$ having tame growth of covering numbers.

math.DS↗

arXiv2026

A Hard-Core Subshift Whose Sofic Mean Dimension Depends on the Sofic Approximation

We exhibit a topologically mixing continuous-alphabet subshift of the free group $F_2$ whose sofic mean dimension depends on the chosen homomorphic sofic approximation, which gives an answer of Li \cite[Remark 2.7]{Li13}. The system is the hard-core subshift \[ X_{\rm hc}=\{x\in [0,1]^{F_2}:x_gx_{gs}=0\text{ for every }g\in F_2\text{ and }s\in\{a,b\}\}. \] We construct one sofic approximation from finite quotients compatible with the parity homomorphism $F_2\to\Z/2\Z$; all of its action graphs are bipartite and give sofic mean dimension exactly $1/2$. A second approximation is selected from two independent uniform random permutations and gives a value in $[1/5,9/20]$. Consequently a mixing action can have two distinct positive sofic mean dimensions.

math.DS↗

arXiv2025

Relative entropy, topological pressure and variational principle for locally compact sofic group actions

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 and relative sofic entropy. Moreover, it is shown that the relative variational principle remains valid in this paper. Secondly, the topological pressure for locally compact sofic group actions is investigated and the variational principle for topological pressure in this sofic context is established. As an application, we show a sufficient condition for a signed measure to be a $G$-invariant measure. These contributions generalize the classical results for countable sofic groups on such spaces.

math.DS↗

arXiv2025

Distinct topological excitonic insulators characterized by quantum geometry

Theintertwining of electron-hole correlation and nontrivial topology is known to give rise to exotic topological excitonic insulators. Here, we show that the involvement of quantum geometry can characterize more exotic excitonic phases exhibiting physical properties that are not influenced by their topology but by geometry. Starting from a topological band insulator and gradually reducing the band gap, many-body interaction can initially generate a p + ip-wave and then an s-wave excitonic insulator. Interestingly, they bear the same Chern number but exhibit completely different spin textures and magneto-optical Kerr responses, reflecting the intricate geometric distinctions in their wave functions. We also propose to enhance the correlation effect via Floquet engineering, which provides a systematic way to realize these topological excitonic insulators and their phase transitions in the nonequilibrium steady states. Our results demonstrate correlated phenomena characterized by quantum geometry, beyond the conventional topological classifications.

cond-mat.str-el↗

arXiv2025

Sofic conditional mean dimension, relative sofic mean dimension and their localizations

Let $π:(X,G)\to (Y,G) $ be a factor map between continuous actions of a sofic group $G$, we study sofic conditional mean dimension and relative sofic mean dimension introduced in \cite{LBB2} and \cite{LB}, respectively. We obtain that if $π$ has non-negative sofic conditional mean dimension (resp. relative sofic mean dimension), then $π$ has the maximal zero sofic conditional mean dimension factor (resp. maximal relative zero sofic mean dimension factor). Additionally, the local properties of sofic conditional mean dimension and relative sofic mean dimension are studied. We introduce the sofic conditional mean dimension tuples and relative sofic mean dimension tuples, and show that $π$ has positive sofic conditional mean dimension (resp. relative sofic mean dimension) if and only if the set of sofic conditional mean dimension tuples (resp. relative sofic mean dimension tuples) is nonempty.

math.DS↗