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math-ph2019
Spectral decimation of the magnetic Laplacian on the Sierpinski gasket: Solving the Hofstadter-Sierpinski butterfly
Joe P. Chen, Ruoyu Guo
The magnetic Laplacian (also called the line bundle Laplacian) on a connected weighted graph is a self-adjoint operator wherein the real-valued adjacency weights are replaced by un…
math-ph2018
Laplacian growth & sandpiles on the Sierpinski gasket: limit shape universality and exact solutions
Joe P. Chen, Jonah Kudler-Flam
We establish quantitative spherical shape theorems for rotor-router aggregation and abelian sandpile growth on the graphical Sierpinski gasket () when particles are launched fr…