Universality for critical KCM: infinite number of stable directions

@article{Hartarsky2020UniversalityFC,
  title={Universality for critical KCM: infinite number of stable directions},
  author={Ivailo Hartarsky and Laure Marêché and Cristina Toninelli},
  journal={Probability Theory and Related Fields},
  year={2020},
  pages={1-38}
}
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 stochastic version of the family of cellular automata with random initial state known as $${{\mathscr {U}}}$$ U -bootstrap percolation. KCM have an interest in their own right, owing to their use for modelling the liquid-glass transition in condensed matter physics. In two dimensions there are three… 
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References

SHOWING 1-10 OF 43 REFERENCES
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 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
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
Universality for critical kinetically constrained models: infinite number of stable directions
Kinetically constrained models (KCM) are reversible interacting particle systems on Zd with continuous-time constrained Glauber dynamics. They are a natural non-monotone stochastic version of the
Monotone Cellular Automata in a Random Environment
TLDR
The results in this paper are the first of any kind on bootstrap percolation considered in this level of generality, and in particular the first that make no assumptions of symmetry.
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
Glassy Time-Scale Divergence and Anomalous Coarsening in a Kinetically Constrained Spin Chain
We analyse the out of equilibrium behavior of an Ising spin chain with an asymmetric kinetic constraint after a quench to a low temperature T. In the limit T\to 0, we provide an exact solution of the
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
Subcritical -bootstrap percolation models have non-trivial phase transitions
. We prove that there exist natural generalizations of the classical bootstrap percolation model on Z 2 that have non-trivial critical probabilities, and moreover we characterize all homogeneous,
Time Scale Separation and Dynamic Heterogeneity in the Low Temperature East Model
We consider the non-equilibrium dynamics of the East model, a linear chain of 0–1 spins evolving under a simple Glauber dynamics in the presence of a kinetic constraint which forbids flips of those
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