Scaling limit of the sandpile identity element on the Sierpinski gasket
Abstract
We investigate the identity element of the sandpile group on finite approximations of the Sierpinski gasket with normal boundary conditions and show that the sequence of piecewise constant continuations of the identity elements on SGn converges in the weak* sense to the constant function with value 4 on the Sierpinski gasket SG. We then generalize the proof to a wider range of functions and obtain the scaling limit for the identity elements with different choices of sink vertices.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.