6 problems

Let $G=(V\cup\{s\},E)$ be a finite graph with designated sink vertex $s$, and let $\rho_G(p)$ denote the stationary average density for the $p$-toppling rule, where $p\in[0,1]$ and…

Maximum periodicity conjecture. The maximum periodicity of any vertex $v$ in each listed fractal graph is given by the corresponding value above.

Perrot–Pham's conjecture. The polynomial $\mathcal B(G,s;y)$ is independent of the choice of the sink vertex $s$.

Let $\Gamma'$ be a decoration of a $d$-regular tree, and let $g(x)$ be the generating function for weighted clusters containing the origin. Let $D$ denote the exponential growth fa…

Let $\Gamma$ be an infinite $d$-regular tree, and let $\Gamma'$ be a graph quasi-isometric to $\Gamma$, including a decoration of $\Gamma$. The cell-wise first-wave critical expone…

Let $\Gamma$ be an infinite $d$-regular tree, and let $\Gamma'$ be a graph quasi-isometric to $\Gamma$, including a decoration of $\Gamma$. A critical exponent is the power-law exp…