Volker Betz

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20242026

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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.PR2024

Loop percolation versus link percolation in the random loop model

Volker Betz, Andreas Klippel, Mino Nicola Kraft

In [Muhl2019], Peter Mühlbacher showed that in the random loop model without loop weights, a loop phase transition (assuming it exists) cannot occur at the same parameter as the pe…

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

Loop percolation versus link percolation in the random loop model

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