Integral Kernels on Complex Symmetric Spaces and for the Dyson Brownian Motion

2020/12/20 by Piotr Graczyk, Graczyk, P., P Sawyer +1
Economics, Econometrics and Finance · Mathematics · #31B05 #31B25 #53C35 #60J50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2012.10946

openalex publication_date 2020/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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