On eigenvalue problems for the random walks on the Sierpinski pre-gaskets
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We work with increasing finite setsV m called pre-gaskets approximating the finite Sierpinski gasket located inR N−1 (N ≥ 3). The eigenvalues of the discrete Laplacian onV m under the Dirichlet and Neumann boundary conditions are completely determined using the decimation method due to Rammal.
Key wordseigenvalues Sierpinski pre-gasket decimation method
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- R. Rammal and G. Toulouse, Random walks on fractal structures and percolation clustars. J. Physique Lett.,43 (1982), L13-L22.Google Scholar