# Kinetically Constrained Models with Random Constraints

## TL;DR

This paper investigates how random environments influence the dynamics of kinetically constrained models, specifically analyzing time scales like bootstrap percolation and relaxation times in two mixed models on 2.

## Contribution

It introduces and analyzes two new kinetically constrained models with random environments, comparing their time scales and effects of randomness on dynamics.

## Key findings

- Random environment significantly affects relaxation times.
- Differences observed between bootstrap percolation and relaxation times.
- Random constraints alter the time for emptying the origin.

## 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.