Pfaffian Formulae for One Dimensional Coalescing and Annihilating Systems
Pfaffian Formulae for One Dimensional Coalescing and Annihilating Systems
复制标题
一维聚结和湮灭系统的普法夫公式
DOI：
10.1214/ejp.v16-942
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发表时间：
2010
影响因子：
1.4
通讯作者：
O. Zaboronski
中科院分区：
文献类型：
--
作者：
R. Tribe;O. Zaboronski
本文考虑了实线上一维布朗粒子系统的瞬间聚合或瞬间湮灭问题。在最大入射定律下，证明了粒子在固定时刻的分布是与描述实Ginibre随机矩阵系综实特征值一维分布的Pfaffian点过程密切相关的。作为应用，导出了聚结粒子的n点密度函数的精确大时间渐近性。
The paper considers instantly coalescing, or instantly annihilating, systems of one-dimensional Brownian particles on the real line. Under maximal entrance laws, the distribution of the particles at a fixed time is shown to be Pfaffian point processes closely related to the Pfaffian point process describing one dimensional distribution of real eigenvalues in the real Ginibre ensemble of random matrices. As an application, an exact large time asymptotic for the $n$-point density function for coalescing particles is derived.