Internal DLA on cylinder graphs: fluctuations and mixing
Internal DLA on cylinder graphs: fluctuations and mixing
We use coupling ideas introduced in [13] to show that an IDLA process on a cylinder graph $G\times {\mathbb {Z}} $ forgets a typical initial profile in $\mathcal {O}( N\sqrt {\tau _{N}} (\log \! N)^{2} )$ steps for large $N$, where $N$ is the size of the base graph $G$, …