# 3

## The mixing time of the swap (switch) Markov chains: a unified approach

We show that the swap Markov chain is rapidly mixing on $P$-stable degree sequences of simple, bipartite, and directed graphs. Consequently, we have rapid mixing on power-law distribution-bounded degree sequences with parameter $\gamma2$ and on …

## Computing the Difficulty of Critical Bootstrap Percolation Models is NP-hard

Bootstrap percolation is a class of cellular automata with random initial state. Two-dimensional bootstrap percolation models have three universality classes, the most studied being the 'critical' one. For this class the scaling of the quantity of …