UMR 5584

# Long Brownian bridges in hyperbolic spaces converge to Brownian trees

### Mercredi 15 novembre 10:30-11:30 - XinXin CHEN - ICJ Université Lyon 1

Long Brownian bridges in hyperbolic spaces converge to Brownian trees

Résumé : We consider the long Brownian bridge started from the origin in hyperbolic space H^d and show that its range, after being suitably renormalised, converges in law to a Brownian continuum tree in the sense of Gromov-Hausdorff. The rough idea of the proof will be talked about, by presenting the convergence, obtained by Bougerol and Jeulin [1], 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 infinite Brownian loop in hyperbolic space.
References
[1] Bougerol, P. and Jeulin, T. (1999) Brownian bridge on hyperbolic spaces and on homogeneous trees. Probab. Theory Related Fields. 115(1), 95-120.

Pour en savoir plus sur cet événement, consultez l'article Séminaires SPOC