Combinatorics for general kinetically constrained spin models

Laure Marêché (1)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

We study the set of possible configurations for a general kinetically constrained model (KCM), a non monotone version of the 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 Marêché, Martinelli and Toninelli to complete the proof of a conjecture put forward by Morris.

Mots clés: Kinetically constrained models; Bootstrap percolation; East model

Domaines: Probabilités [math.PR]; Combinatoire [math.CO]

Laure Marêché. Combinatorics for general kinetically constrained spin models. SIAM Journal on Discrete Mathematics, 2020, 34 (1), pp.370-384. ⟨10.1137/18M1231134⟩. ⟨hal-01567129v2⟩