Author

R. Kaiser

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Preprint Sep 2026

Limit shape, avalanches, and stabilisation of abelian sandpiles on comb lattices

We study two aspects of the abelian sandpile model on comb lattices. First, we prove that the infinite-volume limit of the stationary measures is supported on the saturated configuration. We then investigate the shape of avalanches induced by adding a particle at the origin in finite boxes of size $(2n+1)\times(2n+1)$...

Robin Kaiser, Ecaterina Sava-Huss, J. Überbacher · 1 citation · ⚡1

Preprint Jul 2026

Phase transition for the asymptotic entropy of branching random walks on groups

We consider supercritical branching random walks (BRW) on countable groups $G$ and we prove that the asymptotic entropy of the empirical distributions of the BRW has a phase transition at $\rho_* = e^{h(\mu)}$, where $h(\mu)$ is the asymptotic entropy of the underlying random walk on $G$ with step distribution $\mu$. B...

Jérémie Brieussel, R. Kaiser, Martin Klötzer et al. · 0 citations