Mihail–Vazirani conjecture on rapid mixing of the matroid basis-exchange walk

Let $M=(X,\mathcal{I})$ be a matroid, and let its bases be its maximal independent sets. The base-exchange walk is the random walk on the bases of $M$ that removes a uniformly chosen element from the current base and then chooses a new base containing the resulting independent set. Mihail–Vazirani conjecture. The base-exchange walk converges rapidly. The paper explicitly states that Anari, Liu, Gharan, and Vinzant resolved this conjecture using rapid convergence of the down-up walk on local spectral expanders, so the conjecture is solved.