We introduce geometric comparison inequalities that give bounds on the eigenvalues of a reversible Markov chain in terms of the eigenvalues of a second chain. The bounds are applied to get sharp results for the exclusion process.
"Comparison Theorems for Reversible Markov Chains." Ann. Appl. Probab. 3 (3) 696 - 730, August, 1993. https://doi.org/10.1214/aoap/1177005359