Abstract
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 performing it, based on a novel two-block dynamics with a probabilistic proof instead of the original spectral one. We illustrate the method by very directly proving an upper bound on the relaxation time of KCM like the one for the East model in a strikingly general setting. Namely, we treat KCM on finite or infinite one-dimensional volumes, with any boundary condition, conditioned on any of the irreducible components of the state space, with arbitrary site-dependent state spaces and, most importantly, arbitrary inhomogeneous rules.
Funding Statement
This work is supported by ERC Starting Grant 680275 “MALIG.”
Acknowledgments
We thank Cristina Toninelli for stimulating discussions and helpful remarks. We are also grateful to the anonymous referee for careful proofreading and helpful comments on the presentation of the paper.
Citation
Ivailo Hartarsky. "Bisection for kinetically constrained models revisited." Electron. Commun. Probab. 26 1 - 10, 2021. https://doi.org/10.1214/21-ECP434
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