广义零程粒子系统的生成元及试验函数空间

Test function space for generator of generalized infinite particle system with zero range interactions

具有零程相互作用的无穷粒子系统最早由SpitzerF引入,它描述了这样一种随机模型, 在可列个位置上有无穷个不可辨粒子做随机的移动,同一时刻任何位置上最多只能发生一个粒子转移. 研究了在同一时刻任一位置上可以发生任意有限个粒子转移的情形, 给出了系统的生成元及试验函数空间,使用的主要方法为泛函分析的方法. 试验表明当每次转移多个粒子时,系统生成元的定义域在试验函数空间是稠密的,系统的生成元是适定的.

An infinite particle system with zero range interactions was first introduced by Frank Spitzer. It described such a stochastic model that there were infinite unrecognized particles moving with random at infinite sequence of sites. At the same time there was only one particle moving from one site to another. It was studied that at the same time there were any finite particles moving from one site to another. The generator and test function space were determined mainly by functional analysis. Results indicate that when particles are moving, the domain of generator is dense in the test function space and the generator of the system is well defined.