# Combinatorics for General Kinetically Constrained Spin Models

@article{Mareche2020CombinatoricsFG, title={Combinatorics for General Kinetically Constrained Spin Models}, author={Laure Marêché}, journal={SIAM J. Discret. Math.}, year={2020}, volume={34}, pages={370-384} }

We study the set of possible configurations for a general kinetically constrained model (KCM), a non monotone version of the $\mathcal{U}$-bootstrap percolation cellular automata. We solve a combinatorial question that is a generalization of a problem addressed by Chung, Diaconis and Graham in 2001 for a specific one-dimensional KCM, the East model. Since the general models we consider are in any dimension and lack the oriented character of the East dynamics, we have to follow a completely…

## 5 Citations

Exact asymptotics for Duarte and supercritical rooted kinetically constrained models

- Mathematics
- 2018

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…

U-bootstrap percolation: Critical probability, exponential decay and applications

- MathematicsAnnales 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…

Refined universality for critical KCM: lower bounds

- MathematicsCombinatorics, Probability and Computing
- 2022

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.…

Bisection for kinetically constrained models revisited

- MathematicsElectronic Communications in Probability
- 2021

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 new way of…

Refined universality for critical KCM: upper bounds

- Mathematics
- 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.…

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