• Corpus ID: 233033864

Refined universality for critical KCM: upper bounds

@inproceedings{Hartarsky2021RefinedUF,
  title={Refined universality for critical KCM: upper bounds},
  author={Ivailo Hartarsky},
  year={2021}
}
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 bootstrap percolation. There are three classes of such models [5], the most studied being the critical one. Together with the companion paper by Marêché and the author [15], our work determines the logarithm of the infection time up to a constant factor for all critical KCM, which were previously known only up to… 

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References

SHOWING 1-10 OF 40 REFERENCES
Refined universality for critical KCM: lower bounds
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 bootstrap percolation.
Universality of two-dimensional critical cellular automata
We study the class of monotone, two-state, deterministic cellular automata, in which sites are activated (or `infected') by certain configurations of nearby infected sites. These models have close
Universality for critical KCM: Finite number of stable directions
In this paper we consider kinetically constrained models (KCM) on Z2 with general update families U . For U belonging to the so-called “critical class” our focus is on the divergence of the infection
Exact asymptotics for Duarte and supercritical rooted kinetically constrained models
Kinetically constrained models (KCM) are reversible interacting particle systems on $\mathbb Z^d$ with continuous time Markov dynamics of Glauber type, which represent a natural stochastic (and
Universality for critical KCM: infinite number of stable directions
Kinetically constrained models (KCM) are reversible interacting particle systems on $${{\mathbb {Z}}} ^d$$ Z d with continuous-time constrained Glauber dynamics. They are a natural non-monotone
Towards a universality picture for the relaxation to equilibrium of kinetically constrained models
TLDR
This paper establishes a close connection between the critical scaling of characteristic time scales for KCM and the scaling of the critical length in critical bootstrap models, and applies the general method to the Friedrickson-Andersen k-facilitated models and to the Gravner-Griffeath model.
U-bootstrap percolation: Critical probability, exponential decay and applications
  • Ivailo Hartarsky
  • Mathematics
    Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
  • 2021
Bootstrap percolation is a wide class of monotone cellular automata with random initial state. In this work we develop tools for studying in full generality one of the three `universality' classes of
A sharper threshold for bootstrap percolation in two dimensions
Two-dimensional bootstrap percolation is a cellular automaton in which sites become ‘infected’ by contact with two or more already infected nearest neighbours. We consider these dynamics, which can
Combinatorics for General Kinetically Constrained Spin Models
TLDR
A combinatorial question is solved that is a generalization of a problem addressed by Chung, Diaconis and Graham in 2001 for a specific one-dimensional KCM, the East model, and is used by Mar\^ech\'e, Martinelli and Toninelli to complete the proof of a conjecture put forward by Morris.
Kinetically Constrained Models
Kinetically constrained spin models (KCSM) are interacting particle systems which are intensively studied in physics literature as models for systems undergoing glass or jamming transitions. KCSM
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