Strong Markov property of determinantal processes with extended kernels
Strong Markov property of determinantal processes with extended kernels
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DOI：
10.1016/j.spa.2015.08.003
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发表时间：
2014-12
影响因子：
1.4
通讯作者：
H. Osada;H. Tanemura
中科院分区：
文献类型：
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作者：
H. Osada;H. Tanemura
摘要 非碰撞布朗运动（参数β=2的戴森布朗运动模型）和非碰撞贝塞尔过程是行列式过程。也就是说，它们的时空相关函数由行列式表示。在适当的缩放限制下，例如体积、软边缘和硬边缘缩放限制，这些过程收敛到描述具有无限数量粒子的系统的行列式过程。本文的主要目的是展示这些极限过程的强马尔可夫性质，它们分别是具有扩展正弦核、扩展艾里核和扩展贝塞尔核的行列式过程。我们还确定了与行列式过程相关的拟正则狄利克雷形式和无限维随机微分方程。
Abstract Noncolliding Brownian motion (Dyson’s Brownian motion model with parameter β= 2) and noncolliding Bessel processes are determinantal processes; that is, their space–time correlation functions are represented by determinants. Under a proper scaling limit, such as the bulk, soft-edge and hard-edge scaling limits, these processes converge to determinantal processes describing systems with an infinite number of particles. The main purpose of this paper is to show the strong Markov property of these limit processes, which are determinantal processes with the extended sine kernel, extended Airy kernel and extended Bessel kernel, respectively. We also determine the quasi-regular Dirichlet forms and infinite-dimensional stochastic differential equations associated with the determinantal processes.