Quantum operators in classical probability theory: IV. Quasi-duality and thinnings of interacting particle systems
成果类型：
Article
署名作者：
Sudbury, A; Lloyd, P
署名单位：
Monash University; Monash University
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
发表日期：
1997
页码：
96-114
关键词：
摘要：
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 of single-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.