On the mixing time of coordinate Hit-and-Run

Hariharan Narayanan, Piyush Srivastava

Abstract: We obtain a polynomial upper bound on the mixing time of the coordinate Hit-and-Run (CHR) random walk on an dimensional convex body, where is the number of steps needed to reach within of the uniform distribution with respect to the total variation distance, starting from a warm start (i.e., a distribution which has a density with respect to the uniform distribution on the convex body that is bounded above by a constant). Our upper bound is polynomial in n, R and , where we assume that the convex body contains the unit -unit ball and is contained in its R-dilation . Whether CHR has a polynomial mixing time has been an open question.