Centrum Voor Wiskunde En Informatica on the Existence and Non-existence of Finitary Codings for a Class of Random Fields
Centrum Voor Wiskunde En Informatica on the Existence and Non-existence of Finitary Codings for a Class of Random Fields
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Centrum Voor Wiskunde En Informatica 关于一类随机域的有限编码的存在与不存在
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通讯作者：
Berg Cwi
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作者：
J. Van Den Berg;J. E. Steif;J. Van Den;Berg Cwi
关于一类随机场的有穷性与无穷性研究了有限值独立同分布随机场的有穷性编码（也称有穷性同态或有穷性因子映射）的存在性。处理到特定的随机域。对于马尔可夫随机场，我们表明，使用的想法马顿和希尔兹，存在的相变是一个障碍的存在上述编码：这产生了一个大类的伯努利位移，没有这样的编码存在。相反，我们表明，对于单调指数遍历概率元胞自动机的平稳分布，这样的编码确实存在。编码的构造部分受到用于精确模拟的Propp-Wilson算法的启发。特别地，结合Martinelli和Olivieri的一个定理，我们得到了这样一个事实：对于Zd（d ≥ 2）上的铁磁Ising模型的正态，当相互作用参数低于其临界值时，存在这样的编码，而当相互作用参数高于其临界值时，不存在这样的编码.注：第一作者在项目PNA 3.1“概率“下开展的工作。一个略有不同的版本，这篇论文已被接受出版的概率年鉴。
On the existence and non-existence of finitary for a class of random fields Abstract We study the existence of finitary codings (also called finitary ho-momorphisms or finitary factor maps) from a finite-valued i.i.d. process to certain random fields. For Markov random fields we show, using ideas of Marton and Shields, that the presence of a phase transition is an obstruction for the existence of the above coding: this yields a large class of Bernoulli shifts for which no such coding exists. Conversely, we show that for the stationary distribution of a monotone exponentially ergodic probabilistic cellular automaton such a coding does exist. The construction of the coding is partially inspired by the Propp-Wilson algorithm for exact simulation. In particular, combining our results with a theorem of Martinelli and Olivieri, we obtain the fact that for the plus state for the ferro-magnetic Ising model on Z d , d ≥ 2, there is such a coding when the interaction parameter is below its critical value and there is no such coding when the interaction parameter is above its critical value. Note: Work by the first author carried out under project PNA3.1 " Probability ". A slightly different version of this paper has been accepted for publication in the Annals of Probability.