Combinatorics for general kinetically constrained spin models

Abstract : Bootstrap percolation is a well-known class of monotone cellular automata, in which sites may be infected or not and, at any step, a site becomes infected if a certain constraint is satisfied. Bootstrap percolation has a non-monotone stochastic counterpart , kinetically constrained models (KCM), which were introduced to model the liquid/glass transition, a major open problem of condensed matter physics. In KCM, the state of each site is re-sampled (independently) at rate 1 if the constraint is satisfied. A key problem for KCM is to determine the divergence of timescales as p → 0, where p is the equilibrium density of infected sites. In this article we establish a combinatorial result which in turn allows to prove a lower bound on timescales for KCM.
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Contributeur : Laure Marêché <>
Soumis le : vendredi 21 juillet 2017 - 17:50:50
Dernière modification le : vendredi 4 janvier 2019 - 17:32:34


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  • HAL Id : hal-01567129, version 1


Laure Marêché. Combinatorics for general kinetically constrained spin models. 2017. 〈hal-01567129〉



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