## Completion of $S/I$

Type:
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.