Long Brownian bridges in hyperbolic spaces converge to Brownian trees
主 题: Long Brownian bridges in hyperbolic spaces converge to Brownian trees
报告人: Xinxin Chen (Institut Camille Jordan, Universite Lyon 1)
时 间: 2017-07-25 15:00-16:00
地 点: 理科1号楼1303
Abstract: We consider the long Brownian bridge started from the origin in hyperbolic space Hd and show that its range, after being suitably renormalised, converges in law to a Brownian continuum tree in the sense of Gromov-Hausdor . The rough idea of the proof will be talked about, by presenting the convergence, obtained by Bougerol and Jeulin , of the radial part; the invariance property of re-rooting and the hyperbolicity property. The similar idea will be applied to obtain the local convergence of the in nite Brownian loop in hyperbolic space.