sofic群作用的弱扩张性

具有受控规格和熵膨胀性的非均匀系统的热力学形式

Thermodynamic formalism for non-uniform systems with controlled specification and entropy expansiveness

本文推广Climenhaga-Thompson轨道分解准则和Pavlov的结果，得到非均匀膨胀流（含熵膨胀流）平衡态唯一性，还通过弱Walters条件和高斯-博内型论证给出两个应用实例。

随机算子、谱测度与在索菲克群中的局部经验收敛

Random operators, spectral measures, and local empirical convergence in sofic groups

本文研究了随机算子在索菲克群中的谱分布近似问题，通过局部和经验收敛测度的概念，证明了在有限体积类比下的弱收敛性，并给出了Lück型近似定理及复系数情况下的点wise收敛性。

具有 specification 的 sofic 群膨胀作用、强拓扑马尔可夫性质与满射性

Expansive actions with specification of sofic groups, strong topological Markov property, and surjunctivity

本文证明了对于 sofic 群作用的膨胀动力系统，在非负 sofic 拓扑熵且满足弱 specification 与强拓扑马尔可夫性质的条件下，系统必为满射的。

从LDPC码出发的代数动力系统满足弱Pincker性质的强否定

Algebraic dynamical systems from LDPC codes satisfy a strong negation of the weak Pinsker property

本文通过构造LDPC码相关的代数动力系统，展示了具有完全正熵但无直接伯恩乌利因子的例子，揭示了弱Pincker性质的强否定。

Local weak$^{*}$-Convergence, algebraic actions, and a max-min principle

We continue our study of when topological and measure-theoretic entropy agree for algebraic action of sofic groups. Specifically, we provide a new abstract method to prove that an algebraic action is strongly sofic. The method is based on passing to a "limiting object" for sequences of measures which are asymptotically supported on topological microstates. This limiting object has a natural poset structure that we are able to exploit to prove a max-min principle: if the sofic approximation has ergodic centralizer, then the largest subgroup on which the action is a local weak$^{*}$-limit of mea…

独立元组与Deninger问题

Independence Tuples and Deninger's Problem

受“波兰模型和Sofic熵”中的结果的启发，我们定义了Kerr和Li提出的sofic熵的独立元组的修改版本。这些修改后的版本基本上要求独立序列产生的表示弱包含在左正规时，投影到库普曼表示。利用这一点，我们可以推广我们以前关于Deninger问题的结果。也就是说，如果G是sofic群，且f在M_{n}（Z（G））中且作为l^{2}（G）^{n}上的算子可逆，则f的Fuglede-Kadison行列式为1当且仅当f在M_{n}（Z（G））中可逆.

On sofic groups, Kaplansky's conjectures, and endomorphisms of pro-algebraic groups

Let $G$ be a group. Let $X$ be a connected algebraic group over an algebraically closed field $K$. Denote by $A=X(K)$ the set of $K$-points of $X$. We study a class of endomorphisms of pro-algebraic groups, namely algebraic group cellular automata over $(G,X,K)$. They are cellular automata $τ\colon A^G \to A^G$ whose local defining map is induced by a homomorphism of algebraic groups $X^M \to X$ where $M\subset G$ is a finite memory set of $τ$. Our first result is that when $G$ is sofic, such an algebraic group cellular automaton $τ$ is invertible whenever it is injective and $\text{char}(K)=0…

弱扩张性质与粗扩张共形系统的大偏差原理

Weak expansion properties and a large deviation principle for coarse expanding conformal systems

本文证明粗扩张共形系统在排斥子上具有渐近h-扩张性，并据此建立平衡态存在性及迭代原像的大偏差原理与等分布结果。

Max-Min theorems for weak containment, square summable homoclinic points, and completely positive entropy

We prove a max-min theorem for weak containment in the context of algebraic actions. Namely, we show that given an algebraic action of $G$ on $X,$ there is a maximal, closed $G$-invariant subgroup $Y$ of $X$ so that the action of $G$ on $Y$ is weakly contained in a Bernoulli shift. This subgroup is also the minimal subgroup so that any action weakly contained in a Bernoulli shift is $G\curvearrowright X/Y$-ergodic "in the presence of $G\curvearrowright X$". We give several applications, including a major simplification of the proof that measure entropy equals topological entropy for principal …