Scaling limit for Brownian motions on the $l$-level Sierpinski gaskets: The fractal to Euclidean crossover

David A. Croydon, Ben Hambly, Takashi Kumagai

In two dimensions, the $l$-level Sierpinski gasket $\mathrm{SG}(l)$ is obtained by splitting an equilateral triangle into a collection of $l^2$ equilateral triangles of equal size…