Quantum operators in classical probability theory. IV. Quasi-duality and thinnings of interacting particle systems
Quantum operators in classical probability theory. IV. Quasi-duality and thinnings of interacting particle systems
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经典概率论中的量子算子。
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
Peter Lloyd
中科院分区：
文献类型：
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作者：
Aidan Sudbury;Peter Lloyd
对偶性是研究相互作用粒子系统的一种有效方法。这个概念可以被扩大，并且在以前认为不相关的各种IPS对之间定义了准对偶。因此，可以推导出与对偶性类似的定理。准对偶性的概念自然来自于我们以前在本系列第二篇论文中对单点算子（一个从量子物理学中借用的想法）的研究。它表明，准对偶的一个必要条件是，相应的两个网站的无穷小生成元的特征值是相同的，并利用这一观察，一些准对偶对已被发现和研究。它进一步表明，如果两个不同的IPS共享一个共同的对偶，那么一个可以被认为是一个薄的其他。
Duality has proved to be a powerful technique in the study of interacting particle systems (IPS). This concept can be enlarged and a quasi-duality defined between various pairs of IPS previously thought unrelated. Consequently, theorems of a similar style to those involving duality can be deduced. The concept of quasi-duality follows naturally from our previous studies into the use ofsingle-site operators (an idea borrowed from quantum physics) in paper II of this series. It is shown that a necessary condition for quasi-duality is that the eigenvalues of the corresponding two-site infinitesimal generators be the same, and, using this observation, a number of quasi-dual pairs have been found and studied. It is further shown that if two different IPS share a common dual, then one can be considered as a thinning of the other.