Cutoff for non-negatively curved Markov chains

Understand

Discovered in the context of card shuffling by Aldous, Diaconis and Shahshahani, the cutoff phenomenon has since then been established in a variety of Markov chains.

• However, proving cutoff remains a delicate affair, which requires a detailed knowledge of the chain.
• Identifying the general mechanisms underlying this phase transition -- without having to pinpoint its precise location -- remains one of the most fundamental open problems in the area of mixing times.
• In the present paper, we make a step in this direction by establishing cutoff for Markov chains with non-negative curvature, under a suitably refined product condition.