weakness of the paper. Questions: * In which cases the assumptions of theorems 3,4 hold? In addition to SLC, they have some matroid related assumptions. Since these results intend to demonstrate the power of the SLC class, these should be discussed in more detail. * How the diversity related \alpha enters the mixing bounds? It seems that the bound depends very weakly on \alpha only through \nu(S_0). Edit following author's response: I'm inclined to keep my score of 6. This is due to following reasons: 1) I still find the theoretical contribution ok but not particularly strong, given existing results. As mentioned in the review, it is a weak, unpractical bound, and the proof, in itself, does not provide particular mathematical novelty. 2) The claims that "in practice the mixing time is even better" are not nearly sufficiently supported by the experiments, and therefore the evidence provided to practitioners is very limited. 3) My question regarding dependence on $\alpha$ was not answered in a satisfactory manner. I would expect a more explicit dependence on $\alpha$, since with higher diversity the problem should be more complicated. If this is not reflected in the bounds, it means the bounds are very loose.
1) I still find the theoretical contribution ok but not particularly strong, given existing results. As mentioned in the review, it is a weak, unpractical bound, and the proof, in itself, does not provide particular mathematical novelty.