M. Cabezas

collaborators

4 papers

math.PR2026

Range convergence and sharp one-arm asymptotics for the critical percolation cluster in high dimensions

M. Cabezas, D. Croydon, A. Fribegh +2

For critical Bernoulli bond percolation on $Z^{d}$ in the high-dimensional regime, we prove that the rescaled empirical measure of the cluster of the origin converges, in a suitable…

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

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…