Dual graphs and modified Barlow--Bass resistance estimates for repeated barycentric subdivisions

25 Jun 2018 Kelleher Daniel J. Brzoska Antoni Panzo Hugo Teplyaev Alexander

We prove Barlow--Bass type resistance estimates for two random walks associated with repeated barycentric subdivisions of a triangle. If the random walk jumps between the centers of triangles in the subdivision that have common sides, the resistance scales as a power of a constant $\rho$ which is theoretically estimated to be in the interval $5/4\leqslant\rho\leqslant3/2$, with a numerical estimate $\rho\approx1.306$... (read more)

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