Yi-Tong Yin

Sampling Matchings in Near-linear Time

For every fixed activity $\lambda>0$, we establish three results for the monomer--dimer model on an $n$-vertex simple graph $G$ with $m\ge1$ edges and maximum degree $\Delta$. 1. Near-linear mixing and sampling. Single-edge Glauber dynamics has mixing time $O_\lambda(m[\log^2 n+\log(1/\varepsilon)])$, giving a near-lin...