Bisection for kinetically constrained models revisited

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 new way performing it, based on novel two-block dynamics with probabilistic proof instead the original spectral one. We illustrate by very directly proving an upper bound relaxation time KCM like one East model in strikingly general setting. Namely, treat finite or infinite one-dimensional volumes, any boundary condition, conditioned irreducible components state space, arbitrary site-dependent spaces and, most importantly, inhomogeneous rules.