关于sofic移位轨道增长的一个简短注记

Some notes on the classification of shift spaces: Shifts of Finite Type; Sofic Shifts; and Finitely Defined Shifts

The aim of this article is to find appropriate definitions for shifts of finite type and sofic shifts in a general context of symbolic dynamics. We start showing that the classical definitions of shifts of finite type and sofic shifts, as they are given in the context of finite-alphabet shift spaces on the one-dimensional monoid $\mathbb{N}$ or $\mathbb{Z}$ with the usual sum, do not fit for shift spaces over infinite alphabet or on other monoids. Therefore, by examining the core features in the classical definitions of shifts of finite type and sofic shifts, we propose general definitions tha…

对论文《移位空间分类的若干注记：有限型移位；索菲克移位；以及有限定义移位》的勘误 [Bulletin of the Brazilian Mathematical Society, New Series (2022), 53, 981-1031]

Corrigendum to the paper 'Some notes on the classification of shift spaces: Shifts of Finite Type; Sofic Shifts; and Finitely Defined Shifts' [Bulletin of the Brazilian Mathematical Society, New Series (2022), 53, 981-1031]

本文对移位空间分类研究中的引理5.3进行勘误，并相应修正依赖该引理的后续结果陈述与证明。

Sofic homological invariants and the Weak Pinsker Property

A probability-measure-preserving transformation has the Weak Pinsker Property (WPP) if for every $ε>0$ it is measurably conjugate to the direct product of a transformation with entropy $<ε$ and a Bernoulli shift. In a recent breakthrough, Tim Austin proved that every ergodic transformation satisfies this property. Moreover, the natural analog for amenable group actions is also true. By contrast, this paper provides a counterexample in which the group $Γ$ is a non-abelian free group and the notion of entropy is sofic entropy. The counterexample is a limit of hardcore models on random regular gr…

Orbit equivalence and sofic approximation

Given an ergodic probability measure preserving dynamical system $\G\acts (X,μ)$, where $\G$ is a finitely generated countable group, we show that the asymptotic growth of the number of finite models for the dynamics, in the sense of sofic approximations, is an invariant of orbit equivalence. We then prove an additivity formula for free products with amenable (possibly trivial) amalgamation. In particular, we obtain purely combinatorial proofs of several results in orbit equivalence theory.

关于某些 sofic shift 的子系统

On the subsystems of certain sofic shifts

本文指出 Krieger (1982) 关于子移位嵌入的充分必要条件定理可推广至以某些类别的 sofic shift 作为目标移位的情形。

关于子位移扰动的注记

A note on the perturbations of subshifts

本文研究了不同类别子位移在禁止包含特定词的序列时的扰动性质，证明了sofic shift的扰动仍为sofic shift，给出了synchronized system保持同步的充分条件，并显式计算了$\mathcal{S}$-gap shift和有限型子位移在扰动下的熵降。