Dual Families of Interacting Particle Systems on Graphs
Dual Families of Interacting Particle Systems on Graphs
复制标题
图上相互作用粒子系统的对偶族
DOI：
--
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
Aidan Sudbury
中科院分区：
文献类型：
--
作者：
Aidan Sudbury
给出了具有最近邻相互作用的IPS（相互作用粒子系统）自对偶的简单条件。由此可见，任何有接触转变且没有自发产生的 IPS 都是自对偶的。结果表明，存在 IPS 系列，其中每个 IPS 都是对偶的，并且对于每对 IPS，一个是另一个的“稀疏”。此外，当以生存概率表示时，所有此类 IPS 都具有相同的平衡分布形式。随后是一系列初始无限测量的收敛结果。
A simple condition for IPS (Interacting Particle Systems) with nearest neighbor interactions to be self-dual is given. It follows that any IPS with the contact transition and no spontaneous birth is self-dual. It is shown that families of IPS exist in which every IPS is dual to every other, and such that for every pair of IPS, one is a “thinning” of the other. Further, all such IPS have the same form for an equilibrium distribution when expressed in terms of survival probabilities. Convergence results from a wide class of initial infinite measures follow.