Kinetically Constrained Models with Random Constraints

Abstract

We study two kinetically constrained models in a quenched random environment. The first model is a mixed threshold Fredrickson-Andersen model on ${\mathbb{Z}}^2$, where the update threshold is either $1$ or $2$. The second is a mixture of the Fredrickson-Andersen $1$-spin facilitated constraint and the North-East constraint in ${\mathbb{Z}}^2$. We compare three time scales related to these models - the bootstrap percolation time for emptying the origin, the relaxation time of the kinetically constrained model, and the time for emptying the origin of the kinetically constrained model - and understand the effect of the random environment on each of them.