Spatial mixing and nonlocal Markov chains
Spatial mixing and nonlocal Markov chains
复制标题
空间混合和非局部马尔可夫链
DOI：
10.1002/rsa.20844
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发表时间：
2017
影响因子：
1
通讯作者：
Eric Vigoda
中科院分区：
文献类型：
--
作者：
Antonio Blanca;P. Caputo;A. Sinclair;Eric Vigoda
We consider spin systems with nearest‐neighbor interactions on an n‐vertex d‐dimensional cube of the integer lattice graph Zd . We study the effects that the strong spatial mixing condition (SSM) has on the rate of convergence to equilibrium of nonlocal Markov chains. We prove that when SSM holds, the relaxation time (i.e., the inverse spectral gap) of general block dynamics is O(r), where r is the number of blocks. As a second application of our technology, it is established that SSM implies an O(1) bound for the relaxation time of the Swendsen‐Wang dynamics for the ferromagnetic Ising and Potts models. We also prove that for monotone spin systems SSM implies that the mixing time of systematic scan dynamics is O(logn(loglogn)2) . Our proofs use a variety of techniques for the analysis of Markov chains including coupling, functional analysis and linear algebra.
SwendsenâWang 和 heatâbath 动力学比较
影响因子：
1
作者：
M. Ullrich
通讯作者：
M. Ullrich
Swendsen-Wang 比单键动力学更快
DOI：
10.1137/120864003
发表时间：
2014
期刊：
SIAM J. Discret. Math.
影响因子：
--
作者：
M. Ullrich
通讯作者：
M. Ullrich