Extending sharp random-scan Gibbs spectral gap bounds beyond strong log-concavity via bounded perturbations

Determine whether the spectral gap bounds for the random-scan Gibbs sampler proved under strong log-concavity and log-smoothness extend to targets that are bounded perturbations of strongly log-concave distributions in the sense of Holley–Stroock.

Background

Sharp spectral gap bounds for random-scan Gibbs have been established under strong log-concavity and log-smoothness.

The authors question whether such results persist under bounded perturbations (Holley–Stroock), which is a common robustness notion in MCMC theory.