Christian Mönch

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math.PR2026

Recurrence of strong-decay inhomogeneous long-range percolation clusters

Johannes Bäumler, Lukas Lüchtrath, Christian Mönch

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: lo…

math.PR2026

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

Christian Mönch

We consider a fractional Brownian motion $B$ with Hurst index $0 < H < 1/2$ , and its maximiser $τ$ on $[0, 1]$ . We show that the rescaled process $a^{H} (B_{τ + \cdot / a} - B_{τ})$ converges…

math.PR2026

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

Volker Betz, Alexander Drewitz, Andreas Klippel +1

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…

math.PR2026

Partial orders and monotonicity of logarithmic depth and height in preferential attachment trees

Christian Mönch

We study preferential attachment trees with general attachment rules. A natural intuition is that rewarding high-degree vertices more strongly should make the tree shallower. We te…

Recurrence of strong-decay inhomogeneous long-range percolation clusters

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

(Non-)coincidence of critical parameters for Poisson Zoos and Loop Soup Percolation on Zd, d>4, and Td​,d≥3

Partial orders and monotonicity of logarithmic depth and height in preferential attachment trees

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