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

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 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 .
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https://hal.archives-ouvertes.fr/hal-01789322
Contributor : Piotr Graczyk <>
Submitted on : Wednesday, May 9, 2018 - 9:48:13 PM
Last modification on : Monday, March 9, 2020 - 6:15:57 PM
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  • HAL Id : hal-01789322, version 1

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Piotr Graczyk, P Sawyer. INTEGRAL KERNELS ON COMPLEX SYMMETRIC SPACES AND FOR THE DYSON BROWNIAN MOTION. 2018. ⟨hal-01789322⟩

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