Bisection for kinetically constrained models revisited
arXiv:2104.07883 · doi:10.1214/21-ECP434
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.
arXiv comment9 pages, additional details, improved presentation, extended section 2
References in corpus (8)
- The Asymmetric One-Dimensional Constrained Ising Model
- Universality results for kinetically constrained spin models in two dimensions
- Mixing times of monotone surfaces and SOS interfaces: a mean curvature approach
- Fredrickson-Andersen one spin facilitated model out of equilibrium
- Analysis of top-swap shuffling for genome rearrangements
- Kinetically constrained spin models on trees
- Kinetically Constrained Models with Random Constraints
- Combinatorics for general kinetically constrained spin models