论文标题
HyperCube上环状动力学的截止现象
Cutoff Phenomenon for Cyclic Dynamics on Hypercube
论文作者
论文摘要
已经观察到了马尔可夫动力学的截止现象，并为多种模型进行了严格验证，尤其是用于自旋系统上的Glauber型动力学。但是，先前的研究几乎不考虑不可逆的链。在这项工作中，在HyperCube $σ_{n} = q^{v_ {n}} $上研究了某些环状动力学的截止现象，其中$ q = \ {1，2，3 \} $和$ v_ {n} = n} = \ {1，...这些动力学的主要特征是它们由不可逆转的马尔可夫链表示。基于先前对Curie-Weiss-Potts模型的截止现象的耦合修改，提出了全面的证明。
The cutoff phenomena for Markovian dynamics have been observed and rigorously verified for a multitude of models, particularly for Glauber-type dynamics on spin systems. However, prior studies have barely considered irreversible chains. In this work, the cutoff phenomenon of certain cyclic dynamics are studied on the hypercube $Σ_{n} = Q^{V_{n}}$, where $Q = \{1, 2, 3\}$ and $V_{n} = \{1,...,n\}$. The main feature of these dynamics is the fact that they are represented by an irreversible Markov chain. Based on the coupling modifications suggested in a previous study of the cutoff phenomenon for the Curie-Weiss-Potts model, a comprehensive proof is presented.
