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Weighted isoperimetry implies percolation
Ivailo Hartarsky, Franco Severo, Augusto Teixeira
Consider an infinite edge-weighted graph satisfying an isoperimetric inequality of the type for some , where denotes the weighte…
Super-Arrhenius relaxation of the triangular plaquette model in any dimension
Laurent Bartholdi, Ivailo Hartarsky, Ivan Mitrofanov
Consider the following plaquette model from statistical physics: a lamp lies at every vertex of the triangular lattice and a switch lies at every even vertex of the (bipartite) dua…
Sharpness of the phase transition for constrained-degree percolation
Ivailo Hartarsky, Roger W. C. Silva
We consider constrained-degree percolation on the hypercubic lattice. Initially, all edges are closed, and each edge independently attempts to open at a uniformly distributed rando…
Crossings and diffusion in Poisson driven marked random connection models
Alessandra Faggionato, Ivailo Hartarsky
We first study crossing statistics in random connection models (RCM) built on marked Poisson point processes on . Under general assumptions, we show exponential tail b…
Bootstrap percolation is local
Ivailo Hartarsky, Augusto Teixeira
Metastability thresholds lie at the heart of bootstrap percolation theory. Yet proving precise lower bounds is notoriously hard. We show that for two of the most classical models,…
Catalan percolation
Eleanor Archer, Ivailo Hartarsky, Brett Kolesnik +3
In Catalan percolation, all nearest-neighbor edges along are initially occupied, and all other edges are open independently with probability . Open edges…