论文标题
复杂对称空间和戴森·布朗运动的整体内核
Integral Kernels on Complex Symmetric Spaces and for the Dyson Brownian Motion
论文作者
论文摘要
在本文中，我们在复杂的情况下考虑了平坦和弯曲的riemannian对称空间，并研究了它们的基本积分内核，在潜在和球形分析中：Heat，Newton，Poisson内核和球形函数，即球形傅立叶变换的内核。 我们通过交替的总和公式介绍并利用了这些$ W $ invariant内核的简单新方法。然后，我们使用这些内核的交替总和表示来获得它们的渐近行为。我们将结果应用于$ r^d $的Dyson Brownian Motion。
In this article, we consider flat and curved Riemannian symmetric spaces in the complex case and we study their basic integral kernels, in potential and spherical analysis: heat, Newton, Poisson kernels and spherical functions, i.e. the kernel of the spherical Fourier transform. We introduce and exploit a simple new method of construction of these $W$-invariant kernels by alternating sum formulas. We then use the alternating sum representation of these kernels to obtain their asymptotic behavior. We apply our results to the Dyson Brownian Motion on $R^d$.
