Uniqueness of Brownian motion on Sierpinski carpets
By Martin T. Barlow, Richard F. Bass, Takashi Kumagai, Alexander Teplyaev. 2008
154 citations recorded by the source corpus.
We prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpinski 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.
Subfields: Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/2de889690139137e254cdd367f88e3eec10cddd8
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mathematical Physics
- Alexander Grigorʼyan
- Jiaxin Hu
- András Telcs
- Patricia Alonso-Ruiz
- Luke G. Rogers
- Fabrice Baudoin
- Li Chen
- Alexander Teplyaev
In Statistics and Probability
Citations in the corpus
- Besov class via heat semigroup on Dirichlet spaces II: BV functions and Gaussian heat kernel estimates (2018, background): “The most basic examples of such spaces are generalized Sierpinski carpets, for which there exists a unique Dirichlet form and diffusion processes, see [19], and there is a comprehensive description of properties of the heat operator due to Barlow and Bass [15, 16].”
- Heat Kernels and Green Functions on Metric Measure Spaces (2014, methodology): “For example, the proof of the uniqueness of Brownian motion on Sierpinski carpet in [7] uses Theorem 3.”
- TWO-SIDED ESTIMATES OF HEAT KERNELS ON METRIC MEASURE SPACES (2012, background): “fractals (see [40, 44]) as well as on generalized Sierpinski carpets (see [5, 8]) so that our results apply to such fractals.”