论文标题
Hua-Pickrell半集团的明确表达
Explicit expressions of the Hua-Pickrell semi-group
论文作者
论文摘要
在本文中，我们研究了一维的Hua-Pickrell扩散。我们首先重新审视E. Wong考虑的固定案例，我们为此提供了省略的细节，并通过削减中的相关Legendre函数写下其半组密度的统一表达。接下来，我们关注的是一般（不一定是固定的）情况，我们证明了与不同参数集对应的Hua-Pickrell扩散之间的相互交织关系。另一方面，使用Cauchy Beta Beta积分，另一方面是Girsanov的定理，我们讨论了固定案例和一般情况之间的联系。之后，我们证明了我们的主要结果提供了Hua-Pickrell半组密度的新颖积分表示，回答了Alili，Matsumoto和Shiraishi提出的一个问题（SéminaireDeprobabilités，35，2001）。为此，我们呼吁Maass Laplacian的半集体密度，并将其扩展到磁场的纯构想值。在最后一节中，我们使用Karlin-McGregor公式来得出由T. assiotis引入的多维Hua-Pickrell粒子系统的半组密度的表达。
In this paper, we study the one-dimensional Hua-Pickrell diffusion. We start by revisiting the stationary case considered by E. Wong for which we supply omitted details and write down a unified expression of its semi-group density through the associated Legendre function in the cut. Next, we focus on the general (not necessarily stationary) case for which we prove an intertwining relation between Hua-Pickrell diffusions corresponding to different sets of parameters. Using Cauchy Beta integral on the one hand and Girsanov's Theorem on the other hand, we discuss the connection between the stationary and general cases. Afterwards, we prove our main result providing novel integral representations of the Hua-Pickrell semi-group density, answering a question raised by Alili, Matsumoto and Shiraishi (Séminaire de Probabilités, 35, 2001). To this end, we appeal to the semi-group density of the Maass Laplacian and extend it to purely-imaginary values of the magnetic field. In the last section, we use the Karlin-McGregor formula to derive an expression of the semi-group density of the multi-dimensional Hua-Pickrell particle system introduced by T. Assiotis.
