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A non-P-stable class of degree sequences for which the swap Markov chain is rapidly mixing

One of the simplest methods of generating a random graph with a given degree sequence is provided by the Monte Carlo Markov Chain method using __swaps__. The swap Markov chain converges to the uniform distribution, but generally it is not known …

The mixing time of switch Markov chains: a unified approach

We show that the switch 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 …