Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium.
Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium.
复制标题
快速收敛于均衡的不可逆局部马尔可夫链。
DOI：
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发表时间：
2017
影响因子：
8.6
通讯作者：
W. Krauth
中科院分区：
文献类型：
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作者：
S. Kapfer;W. Krauth
我们研究连续一维硬球模型，并提出不可逆局部马尔可夫链，其混合时间尺度比可逆热浴或 Metropolis 算法更快。混合时间尺度似乎分为两个不同的普遍性类别，两者都比可逆局部马尔可夫链更快。事件链算法是这些马尔可夫链之一的无穷小极限，属于衰减最快的一类。对于硬球模型的晶格气体极限，可逆局部马尔可夫链对应于具有周期性边界条件的对称简单排除过程（SEP）。不可逆马尔可夫链的两个普遍性类别是通过完全不对称的 SEP (TASEP) 和我们在这里提出的更快的变体（提升的 TASEP）来实现的。我们讨论我们的不可逆硬球马尔可夫链如何推广到任意排斥对相互作用，并通过提升马尔可夫链的概念和最近引入的因式分解大都会接受规则转移到更高的维度。
We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heat bath or Metropolis algorithms. The mixing time scales appear to fall into two distinct universality classes, both faster than for reversible local Markov chains. The event-chain algorithm, the infinitesimal limit of one of these Markov chains, belongs to the class presenting the fastest decay. For the lattice-gas limit of the hard-sphere model, reversible local Markov chains correspond to the symmetric simple exclusion process (SEP) with periodic boundary conditions. The two universality classes for irreversible Markov chains are realized by the totally asymmetric SEP (TASEP), and by a faster variant (lifted TASEP) that we propose here. We discuss how our irreversible hard-sphere Markov chains generalize to arbitrary repulsive pair interactions and carry over to higher dimensions through the concept of lifted Markov chains and the recently introduced factorized Metropolis acceptance rule.