20 citations · 130 across the 33 of their papers we have counts for
34 papers
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…
Explosive appearance of cores and bootstrap percolation on lattices
Ivailo Hartarsky, Lyuben Lichev
Consider the process where the vertices of a square -dimensional torus appear consecutively in a random order. We show that typically the size of the -core of the corresp…
Kinetically constrained models
Ivailo Hartarsky, Cristina Toninelli
The goal of this book is to provide an introduction to the mathematical theory of Kinetically constrained models developed in the last twenty years, intended for both mathematician…
Locality approach to the bootstrap percolation paradox
Ivailo Hartarsky, Augusto Teixeira
We revisit the Bootstrap Percolation model, leveraging recent mathematical advances linking it with its local counterpart. This new perspective resolves, for the first time, histor…
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…
Brownian snails with removal die out in one dimension
Ivailo Hartarsky, Lyuben Lichev
Brownian snails with removal is a spatial epidemic model defined as follows. Initially, a homogeneous Poisson process of susceptible particles on with intensity …
Local dimer dynamics in higher dimensions
Ivailo Hartarsky, Lyuben Lichev, Fabio Toninelli
We consider local dynamics of the dimer model (perfect matchings) on hypercubic boxes . These consist of successively switching the dimers along alternating cycles of prescr…
Sensitive bootstrap percolation second term
Ivailo Hartarsky
In modified two-neighbour bootstrap percolation in two dimensions each site of is initially independently infected with probability and on each discrete time step…
Sharp metastability transition for two-dimensional bootstrap percolation with symmetric isotropic threshold rules
Hugo Duminil-Copin, Ivailo Hartarsky
We study two-dimensional critical bootstrap percolation models. We establish that a class of these models including all isotropic threshold rules with a convex symmetric neighbourh…
Kinetically constrained models out of equilibrium
Ivailo Hartarsky, Fabio Toninelli
We study the full class of kinetically constrained models in arbitrary dimension and out of equilibrium, in the regime where the density of facilitating sites in the equilibriu…
The maximal running time of hypergraph bootstrap percolation
Ivailo Hartarsky, Lyuben Lichev
We show that for every , the maximal running time of the -bootstrap percolation in the complete -uniform hypergraph on vertices is . Thi…
Fredrickson--Andersen model in two dimensions
Ivailo Hartarsky, Fabio Martinelli, Cristina Toninelli
The present expository article overviews recent mathematical advances on the Fredrickson--Andersen kinetically constrained spin model in two dimensions. It was introduced in physic…
The normal contraction property for non-bilinear Dirichlet forms
Giovanni Brigati, Ivailo Hartarsky
We analyse the class of convex functionals over for a measure space introduced by Cipriani and Grillo and generalising the classic bilinear…
Subcritical bootstrap percolation via Toom contours
Ivailo Hartarsky, Réka Szabó
In this note we provide an alternative proof of the fact that subcritical bootstrap percolation models have a positive critical probability in any dimension. The proof relies on a…
Bootstrap percolation, probabilistic cellular automata and sharpness
Ivailo Hartarsky
We establish new connections between percolation, bootstrap percolation, probabilistic cellular automata and deterministic ones. Surprisingly, by juggling with these in various dir…
Bisection for kinetically constrained models revisited
Ivailo Hartarsky
The bisection method for kinetically constrained models (KCM) of Cancrini, Martinelli, Roberto and Toninelli is a vital technique applied also beyond KCM. In this note we present a…
Refined universality for critical KCM: upper bounds
Ivailo Hartarsky
We study a general class of interacting particle systems called kinetically constrained models (KCM) in two dimensions. They are tightly linked to the monotone cellular automata ca…
Generalised oriented site percolation
Ivailo Hartarsky, Réka Szabó
We consider a generalised oriented site percolation model (GOSP) on with arbitrary neighbourhood. The key additional difficulties as compared to standard oriented per…
Sharp threshold for the FA-2f kinetically constrained model
Ivailo Hartarsky, Fabio Martinelli, Cristina Toninelli
The Fredrickson-Andersen 2-spin facilitated model on (FA-2f) is a paradigmatic interacting particle system with kinetic constraints (KCM) featuring dynamical facilit…
Refined universality for critical KCM: lower bounds
Ivailo Hartarsky, Laure Marêché
We study a general class of interacting particle systems called kinetically constrained models (KCM) in two dimensions tightly linked to the monotone cellular automata called boots…