Integral kernels on complex symmetric spaces and for the Dyson Brownian Motion. Issue 7 (15th June 2022)

• Record Type: Journal Article
• Authors: Graczyk, P.; Sawyer, P.
• Is Part Of: Mathematische Nachrichten. Volume 295:Issue 7(2022)
• Page Start: 1378
• Page End: 1405
• Publication Date: 2022-06-15
• Subjects: complex symmetric spaces -- Dyson Brownian Motion -- heat kernel -- Newton kernel -- Poisson kernel -- spherical functions; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.201900252
• Languages: English
• ISSNs: 0025-584X

Abstract

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 ${\bf R}^d$ .