Transition density estimates for diffusion processes on homogeneous random Sierpinski carpets

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Spectral asymptotics for Laplacians on self-similar sets (2010, result): “By the results of Barlow and Bass [1, 2, 3, 4] and Kusuoka and Zhou [32, Section 8], there exists a regular Dirichlet form (E ,F) on L2(K, ν) satisfying F ⊂ {u | u : K → R, u is continuous}(=: C(K)) and such that E(u, v) = ∑ i∈S 1 r E(u◦Fi, v◦Fi), u, v ∈ F (1.3) for some r ∈ (0, 1) (note also the re”
Construction of diffusion processes on fractals, $d$-sets, and general metric measure spaces (2005, background): “In [2], [15], [3], [8] a non-degenerate Dirichlet form E ′ on L2(M, ν) is constructed on these spaces, with the property that E ′ is invariant under local isometries of M – and in particular E ′ is the same on each k-complex.”
On the asymptotics of the eigenvalue counting function for random recursive Sierpinski gaskets (2000, background): “There is an alternative randomization for fractals which has been explored in more detail in [10, 3, 12].”
Random Walks on Sierpiński Graphs: Hyperbolicity and Stochastic Homogenization (2003, background): “, see [26], [27] and the references therein).”
On singularity of energy measures on self-similar sets (2005, methodology): “The Harnack inequality is accepted for (E, F) for a general d ≥ 2 ([6, 12 ]); unfortunately, the author is unable to determine whether ( ¯”