Sampling from a Gibbs Measure with Pair Interaction by Means of PCA
Sampling from a Gibbs Measure with Pair Interaction by Means of PCA
复制标题
通过 PCA 从吉布斯测度和配对交互中进行采样
DOI：
10.1007/s10955-012-0612-9
复制
发表时间：
2012
影响因子：
1.6
通讯作者：
E. Scoppola
中科院分区：
文献类型：
--
作者：
Paolo Dai Pra;B. Scoppola;E. Scoppola
本文研究了一般对相互作用下有限体积Gibbs测度的近似采样问题。我们展示了一个并行动力学（概率元胞自动机），有效地实现了采样。在这个动态的产品措施，使新的配置在每个网站包含一个长期的倾向于有利于每个自旋的原始值。这是一个主要的成分，可以证明PCA的平稳分布是接近吉布斯测度的总变差。驱动上述“惯性”项的参数的存在给出了控制动力学的数值实现的并行度的可能性。
We consider the problem of approximate sampling from the finite volume Gibbs measure with a general pair interaction. We exhibit a parallel dynamics (Probabilistic Cellular Automaton) which efficiently implements the sampling. In this dynamics the product measure that gives the new configuration in each site contains a term that tends to favour the original value of each spin. This is the main ingredient that allows one to prove that the stationary distribution of the PCA is close in total variation to the Gibbs measure. The presence of the parameter that drives the “inertial” term mentioned above gives the possibility to control the degree of parallelism of the numerical implementation of the dynamics.