Author

Maximilian Nitzschner

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Preprint Sep 2026

Phase transition for strongly correlated percolation models on supercritical Bernoulli clusters

We consider the level sets of the Gaussian free field and the vacant set of random interlacements, both defined on a typical realization of the infinite cluster of supercritical Bernoulli bond percolation on $\mathbb{Z}^d$, $d \geq 3$. We prove that in the entire supercritical regime of Bernoulli bond percolation, both...

Alberto Chiarini, Zhi-Zhou Liu, Maximilian Nitzschner · 0 citations

Preprint Sep 2026

On the phase transition for the number of collisions on comb graphs

We consider collisions of simple random walks on comb graphs $\mathrm{Comb}(\mathbb{Z},H)$, which are obtained by attaching vertical segments of the form $[0,H_x] \cap \mathbb{Z}$ to any point $x$ of the integer axis. For $\mathrm{Comb}(\mathbb{Z},H)$ with profile $H_x(x) = |x| \log^\gamma(|x| \vee 1)$, we show that tw...

Umberto De Ambroggio, Jenson Ng, Maximilian Nitzschner et al. · 0 citations