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… 
View PDF on arXiv
5 Citations
Background Citations
3

Figures from this paper

5 Citations

Citation Type

Citation Type

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…
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…
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.…
Bisection for kinetically constrained models revisited
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
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.…

References

SHOWING 1-10 OF 20 REFERENCES
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.
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 Results for Kinetically Constrained Spin Models in Two Dimensions
Kinetically constrained models (KCM) are reversible interacting particle systems on $${\mathbb{Z}^{d}}$$Zd with continuous timeMarkov dynamics of Glauber type, which represent a natural stochastic…
Bootstrap percolation, and other automata
Kinetically constrained spin models
We analyze the density and size dependence of the relaxation time for kinetically constrained spin models (KCSM) intensively studied in the physics literature as simple models sharing some of the…
The asymmetric one-dimensional constrained Ising model
We study a one-dimensional spin (interacting particle) system, with product Bernoulli (p) stationary distribution, in which a site can flip only when its left neighbor is in state +1. Such models…
The Asymmetric One-Dimensional Constrained Ising Model: Rigorous Results
AbstractWe study a one-dimensional spin (interacting particle) system, with product Bernoulli (p) stationary distribution, in which a site can flip only when its left neighbor is in state +1. Such…
Facilitated Oriented Spin Models: Some Non Equilibrium Results
We perform the rigorous analysis of the relaxation to equilibrium for some facilitated or kinetically constrained spin models (KCSM) when the initial distribution ν is different from the reversible…
Glassy dynamics of kinetically constrained models
We review the use of kinetically constrained models (KCMs) for the study of dynamics in glassy systems. The characteristic feature of KCMs is that they have trivial, often non-interacting,…
Relaxation to equilibrium of generalized East processes on $\mathbb{Z}^{d}$: Renormalization group analysis and energy-entropy competition
We consider a class of kinetically constrained interacting particle systems on Zd which play a key role in several heuristic qualitative and quantitative approaches to describe the complex behavior…
...
1
2
...