Determinantal martingales and noncolliding diffusion processes
Determinantal martingales and noncolliding diffusion processes
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DOI：
10.1016/j.spa.2014.06.002
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发表时间：
2013-05
影响因子：
1.4
通讯作者：
M. Katori
中科院分区：
文献类型：
--
作者：
M. Katori
非碰撞扩散过程的两个方面已被广泛研究。其中之一是，他们实现为谐波Doob变换的吸收粒子系统的外尔室。另一个方面是可积性，在这个意义上，任何时空相关函数都可以用行列式表示。本文件的目的是澄清这两个方面之间的联系。本文引入了行列式鞅的概念，证明了如果系统具有行列式鞅表示，则系统是行列式的。为了证明这两个方面之间的直接联系，我们研究了三个过程。
Two aspects of noncolliding diffusion processes have been extensively studied. One of them is the fact that they are realized as harmonic Doob transforms of absorbing particle systems in the Weyl chambers. Another aspect is integrability in the sense that any spatio-temporal correlation function can be expressed by a determinant. The purpose of the present paper is to clarify the connection between these two aspects. We introduce a notion of determinantal martingale and prove that, if the system has determinantal-martingale representation, then it is determinantal. In order to demonstrate the direct connection between the two aspects, we study three processes.