Author

C. Mönch

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Preprint Aug 2026

(Non-)coincidence of critical parameters for Poisson Zoos and Loop Soup Percolation on $\mathbb{Z^d}$, $d>4$, and $\mathbb{T}_d$,$ d \ge 3$

In this article we investigate the (non)-coincidence of critical parameters for various related percolation problems. More precisely, for the random walk loop soup we show that on $\mathbb Z^d$, $d\ge 5$, the critical parameters for the percolation problems differ on the discrete graph and the respective metric graph....

Volker Betz, Alexander Drewitz, Andreas Klippel et al. · 0 citations

Preprint Aug 2026

Recurrence of strong-decay inhomogeneous long-range percolation clusters

We prove recurrence criteria for inhomogeneous long-range percolation in dimensions one and two. In dimension one, recurrence follows from a purely geometric scarcity condition: long edges eventually disappear on exponential scales. This applies to weight-dependent random connection models and related one-dimensional s...

Johannes Bäumler, Lukas Lüchtrath, C. Mönch · 0 citations

Preprint Jul 2026

Local structure at the maximum and sharp persistence asymptotics of rough fractional Brownian motion

We consider a fractional Brownian motion $B$ with Hurst index $0<H<1/2$, and its maximiser $\tau$ on $[0,1]$. We show that the rescaled process $a^H(B_{\tau+\,\cdot\,/a}-B_\tau)$ converges in $C_{\mathrm{loc}}(\mathbb R)$ to a limiting tangent law that is $H$-self-similar, supported on nonpositive paths pinned at zero,...

C. Mönch · 0 citations