论文标题
相互作用的粒子系统和雅各比风格的身份
Interacting Particle Systems and Jacobi Style Identities
论文作者
论文摘要
我们考虑到$ \ mathbb {z} $上最近的邻居相互作用的粒子系统的家族，允许$ 0 $，$ 1 $或$ 2 $粒子在网站上。我们为展示产品阻止度量的过程参数广泛的子属性，并显示如何从Balázsand Bowen（2018）的意义上“站起来”。通过比较衡量标准，我们证明了新的三种可变雅各比风格的身份，这与计算具有$ 2 $重复条件的某些广义Frobenius分区有关。通过专门研究特定过程，我们产生了两个可变的身份，这些身份与雅各比三乘积和组合意义的各种身份有关。还考虑了任意$ K $的$ k $ - 排斥流程的家族，并显示出与$ K $重复条件的广义frobenius分区有关的类似的雅各比风格的身份。
We consider the family of nearest neighbour interacting particle systems on $\mathbb{Z}$ allowing $0$, $1$ or $2$ particles at a site. We parametrize a wide subfamily of processes exhibiting product blocking measure and show how this family can be "stood up" in the sense of Balázs and Bowen (2018). By comparing measures we prove new three variable Jacobi style identities, related to counting certain generalised Frobenius partitions with a $2$-repetition condition. By specialising to specific processes we produce two variable identities that are shown to relate to Jacobi triple product and various other identities of combinatorial significance. The family of $k$-exclusion processes for arbitrary $k$ are also considered and are shown to give similar Jacobi style identities relating to counting generalised Frobenius partitions with a $k$-repetition condition.
