Rapid mixing of the down-up walk on matchings of a fixed size

Vishesh Jain, Clayton Mizgerd

Let $G=(V,E)$ be a graph on $n$ vertices and let $m^{\ast }(G)$ denote the size of a maximum matching in $G$. We show that for any $\hat{I}´>0$ and for any $1\le k\le (1-\hat{I}´)m^{\ast }(G)$, the…