INTEGRAL KERNELS ON COMPLEX SYMMETRIC SPACES AND FOR THE DYSON BROWNIAN MOTION

Piotr Graczyk (1) , P Sawyer (2)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 Université Laurentienne, Canada

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 sums. 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 .

Mots clés: Poisson kernel; Newton kernel; heat kernel; spherical functions; Dunkl processes MSC (2010) 31B05; 31B25; 60J50; 53C35

Domaines: Mathématiques [math]; Analyse classique [math.CA]

Piotr Graczyk, P Sawyer. INTEGRAL KERNELS ON COMPLEX SYMMETRIC SPACES AND FOR THE DYSON BROWNIAN MOTION. 2020. ⟨hal-01789322v2⟩