Christian Mönch

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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

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

Christian MÃ¶nch, 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…

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

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 $Z^{d}$ , $d > 4$ , and $T_{d}$ , $d \geq 3$