Uniqueness of Brownian motion on Sierpiński carpets

Barlow, Martin, et al. "Uniqueness of Brownian motion on Sierpiński carpets." Journal of the European Mathematical Society 012.3 (2010): 655-701. <http://eudml.org/doc/277327>.

@article{Barlow2010,
abstract = {We prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpi´nski carpet that is invariant with respect to the local symmetries of the carpet. Consequently, for each such fractal the law of Brownian motion is uniquely determined and the Laplacian is well defined.},
author = {Barlow, Martin, Bass, Richard F., Kumagai, Takashi, Teplyaev, Alexander},
journal = {Journal of the European Mathematical Society},
keywords = {Sierpiński carpet; fractals; diffusions; Brownian motion; uniqueness; Dirichlet forms; Sierpinski carpet; fractals; diffusions, Brownian motion; uniqueness; Dirichlet forms},
language = {eng},
number = {3},
pages = {655-701},
publisher = {European Mathematical Society Publishing House},
title = {Uniqueness of Brownian motion on Sierpiński carpets},
url = {http://eudml.org/doc/277327},
volume = {012},
year = {2010},
}

TY - JOUR
AU - Barlow, Martin
AU - Bass, Richard F.
AU - Kumagai, Takashi
AU - Teplyaev, Alexander
TI - Uniqueness of Brownian motion on Sierpiński carpets
JO - Journal of the European Mathematical Society
PY - 2010
PB - European Mathematical Society Publishing House
VL - 012
IS - 3
SP - 655
EP - 701
AB - We prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpi´nski carpet that is invariant with respect to the local symmetries of the carpet. Consequently, for each such fractal the law of Brownian motion is uniquely determined and the Laplacian is well defined.
LA - eng
KW - Sierpiński carpet; fractals; diffusions; Brownian motion; uniqueness; Dirichlet forms; Sierpinski carpet; fractals; diffusions, Brownian motion; uniqueness; Dirichlet forms
UR - http://eudml.org/doc/277327
ER -