Inhomogeneous Processes with Random One-dimensional Reinforcements

Preprint Oct 2026

Directed fractal percolation and non-Lipschitz variants

While models of undirected and directed geometry in random i.i.d. disorder with rapidly decaying tails are expected to behave similarly and exhibit features of the Kardar--Parisi--Zhang universality class, the scenario when the background noise is fractal is expected to be significantly different. A canonical example o...

S. Ganguly, V. Ginsburg, Kai-Hao Jing · 0 citations

Open access Oct 2026

Critical first passage percolation on random graphs

In 1999, Zhang proved that for first passage percolation on the square lattice Z2 with i.i.d. nonnegative passage times on each edge, if the probability that an edge has zero passage time is exactly 1/2 (the critical threshold for bond percolation on Z2), then the passage time from the origin to the boundary of [−n,n]2...

S. Bhamidi, Rick Durrett, Xiang-Ying Huang · The Annals of Applied Probab... · 0 citations

Preprint Sep 2026

Phase transition for strongly correlated percolation models on supercritical Bernoulli clusters

We consider the level sets of the Gaussian free field and the vacant set of random interlacements, both defined on a typical realization of the infinite cluster of supercritical Bernoulli bond percolation on $\mathbb{Z}^d$, $d \geq 3$. We prove that in the entire supercritical regime of Bernoulli bond percolation, both...

Alberto Chiarini, Zhi-Zhou Liu, Maximilian Nitzschner · 0 citations

Preprint Aug 2026

Near-critical percolation with sparse reinforcements

We study the effect of sparse random reinforcement on near-critical Bernoulli site percolation on the first quadrant of the square lattice. The reinforcement is generated by randomly selecting horizontal and vertical lines and increasing the opening probability $p$ only at their intersections, so that the reinforcement...

Estevão F. Borel, Marcos Sá, R. Sanchis et al. · 0 citations

Preprint Aug 2026

Recurrence of strong-decay inhomogeneous long-range percolation clusters

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: long edges eventually disappear on exponential scales. This applies to weight-dependent random connection models and related one-dimensional s...

Johannes Bäumler, Lukas Lüchtrath, C. Mönch · 0 citations

Preprint Oct 2026

Active lattice percolation: an apparently new universality class of percolation transitions

We investigate a class of dynamic percolation models on a lattice, in which connections are added and removed by a set of local stochastic rules. In particular, the removal of any connection that can result in one connected cluster becoming two (or more) separate clusters is strictly forbidden. These models include and...

V. Hughes, David A. Huse · 0 citations