Sharpness of reversibilization-based bounds for non-reversible Markov chains

Ascertain the sharpness of convergence-rate bounds obtained by applying reversibilized Markov kernels to non-reversible Markov chains on R^d, including their adequacy for mixing time and spectral gap estimates in the non-reversible setting.

Background

For non-reversible chains, several notions of spectral gaps exist, and one common approach is to paper reversibilized kernels to obtain convergence bounds.

The authors note that, despite these approaches, it is not clear whether the resulting bounds are tight in the non-reversible case.