A. Fribergh

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math.PR2025

Bi-infinite incipient cluster in high dimensions

Manuel Cabezas, Alexander Fribergh, Markus Heydenreich +1

We consider high-dimensional percolation at the critical threshold. We condition the origin to be disjointly connected to two points, $x$ and $x^{'}$ , and subsequently take the limit…

math.PR2025

Scaling limit for the random walk on critical lattice trees

GÃ©rard Ben Arous, Manuel Cabezas, Alexander Fribergh

We prove a scaling limit theorem for the simple random walk on critical lattice trees in $Z^{d}$ , for $d \geq 8$ . The scaling limit is the Brownian motion on the Integrated S…

math.PR2025

Random skeletons in high-dimensional lattice trees

Manuel Cabezas, Alexander Fribergh, Mark Holmes +1

We study the behaviour of the rescaled minimal subtree containing the origin and K random vertices selected from a random critical (sufficiently spread-out, and in dimensions d > 8…

math.PR2024

Sharp asymptotics for finite point-to-plane connections in supercritical bond percolation in dimension at least three

Alexander Fribergh, Alan Hammond

We consider supercritical bond percolation in $Z^{d}$ for $d \geq 3$ . The origin lies in a finite open cluster with positive probability, and, when it does, the diameter of…

math.PR2024

Quenched invariance principle for biased random walks in random conductances in the sub-ballistic regime

Alexander Fribergh, Tanguy Lions, Carlo Scali

We consider a biased random walk in positive random conductances on $Z^{d}$ for $d \geq 5$ . In the sub-ballistic regime, we prove the quenched convergence of the properly res…