Poisson kernels of half-spaces in real hyperbolic spaces
Probability
2007-05-23 v1
Abstract
We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space \H^n. This enables us to find asymptotic properties of the kernel. Our starting point is the formula for its Fourier transform. When , 4 or 6 we give an explicit formula for the Poisson kernel itself. In the general case we give various asymptotics and show convergence to the Poisson kernel of \H^n.
Cite
@article{arxiv.math/0503372,
title = {Poisson kernels of half-spaces in real hyperbolic spaces},
author = {T. Byczkowski and P. Graczyk and A. Stos},
journal= {arXiv preprint arXiv:math/0503372},
year = {2007}
}