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arXiv · 1707.06924

Combinatorics for general kinetically constrained spin models

Laure Marêché
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Abstract

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 different route than the one taken by Chung, Diaconis and Graham. Our combinatorial result is used by Mar\^ech\'e, Martinelli and Toninelli to complete the proof of a conjecture put forward by Morris.

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Laure Marêché. 2017-07-21. Combinatorics for general kinetically constrained spin models. https://doi.org/10.1137/18m1231134

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