Before revision:  We show that from a warm start, the random walk mixes in O(n^7) steps where the log factors depend only on constants determined by the warm start and error parameters (and not on the dimension or number of constraints defining the body).
After revision:  We show that from a warm start, the random walk mixes in O(n^7) steps where the log factors depend only on constants associated with the warm start and error parameters (and not on the dimension or number of constraints defining the body).