منابع مشابه
Uniqueness of Brownian motion on Sierpinski carpets
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. Research partially supported by NSERC (Canada), and EPSRC (UK). Research partially...
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We consider random walks on a class of graphs derived from Sierpinski carpets. We obtain upper and lower bounds (which are non-Gaussian) on the transition probabilities which are, up to constants, the best possible. We also extend some classical Sobolev and Poincar e inequalities to this setting.
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Models of complex information processing based on artificial neural networks frequently apply fully connected or random graph structures. However, it is well known that biological neural systems operate on sparsely connected networks having properties quite distinct to random graphs. In this paper, a simple method is introduced for the deterministic generation of strongly connected digraphs. Th...
متن کاملThe Hausdorff Dimension of General Sierpinski Carpets
We refer to R as a general Sierpίήski carpet, after Mandelbrot [4], since Sierpiήski's universal curve is a special case of this construction [6]. It is clear that R = {J[fi(R)9 where r = \R\ and the ft are affine maps contracting R by a factor of n horizontally and m vertically. When n = m these maps are actually similarity transformations, and a well known argument shows the dimension of R is...
متن کاملCoupling and Harnack Inequalities for Sierpinski Carpets
Uniform Harnack inequalities for harmonic functions on the preand graphical Sierpinski carpets are proved using a probabilistic coupling argument. Various results follow from this, including the construction of Brownian motion on Sierpinski carpets embedded in Md , d > 3, estimates on the fundamental solution of the heat equation, and Sobolev and Poincaré inequalities. The Sierpinski carpets (S...
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ژورنال
عنوان ژورنال: Physical Review B
سال: 2016
ISSN: 2469-9950,2469-9969
DOI: 10.1103/physrevb.93.115428