# rapid mixing

## 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 …

## Efficiently sampling the realizations of bounded, irregular degree sequences of bipartite and directed graphs

Since 1997 a considerable effort has been spent on the study of the **swap** (switch) Markov chains on graphic degree sequences. All of these results assume some kind of regularity in the corresponding degree sequences. Recently, Greenhill and …