Bisection for kinetically constrained models revisited

TL;DR

This paper introduces a new probabilistic bisection method for kinetically constrained models, providing a general and flexible approach to analyze relaxation times across various settings.

Contribution

It presents a novel two-block dynamics and a probabilistic proof, extending the bisection method's applicability to diverse KCM configurations.

Findings

Established an upper bound on relaxation time for KCMs like the East model.

Demonstrated the method's applicability to finite and infinite volumes with arbitrary boundary conditions.

Extended the analysis to inhomogeneous and complex KCM rules.

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.