  We study the mixing time of the Dikin walk in a polytope - a random walk
based on the log-barrier from the interior point method literature. This walk,
and a close variant, were studied by Narayanan (2016) and Kannan-Narayanan
(2012). Bounds on its mixing time are important for algorithms for sampling and
optimization over polytopes. Here, we provide a simple proof of their result
that this random walk mixes in time O(mn) for an n-dimensional polytope
described using m inequalities.
