Non-Gaussian upper and lower bounds are obtained for the transition probabilities of the simple random walk on the Sierpinski graph, the pre-fractal associated with the Sierpinski gasket. They are of the same form as bounds previously obtained for the transition density of Brownian motion on the Sierpinski gasket, subject to a scale restriction. A comparison with transition density bounds for random walks on general graphs demonstrates that this restriction represents the scale at which the pre-fractal graph starts to look like the fractal gasket.
Jones, O. D. (1996). Transition probabilities for the simple random walk on the Sierpinski graph. Stochastic Processes and Their Applications, 61(1), 45–69. https://doi.org/10.1016/0304-4149(95)00074-7