Université Paris-Est Université Paris-Est - Marne-la-Vallée Université Paris-Est - Créteil Val-de-Marne Centre National de la Recherche Scientifique

Completion of $S/I$

Site: 
Date: 
13/05/2013 - 11:00 - 12:00
Salle: 
P1-06
Orateur: 
KIGAMI Jun
Localisation: 
Université de Kyoto
Localisation: 
Japon
Résumé: 

We study completion of $S =$ the Sierpinski gasket minus $I =$ the unit interval = the one of the segment of outer triangle of the SG. In the Euclidean distance, the completion is just the SG itself. But if we consider an intrinsic metric on $S/I$, we have di fferent space. In fact, if we consider the Brownian motion on $S/I$, it is "equivalent" to a random walk on a tree and we will get the ternary Cantor set as the Martin boundary. This fact is closely related to the study of a trace of the Brownian motion on the SG to the unit interval.