  The paper concerns a particular example of the Gibbs sampler and its mixing
efficiency. Coordinates of a point are rerandomized in the unit square
$[0,1]^2$ to approach a stationary distribution with density proportional to
$\exp(-A^2(u-v)^2)$ for $(u,v)\in [0,1]^2$ with some large parameter $A$.
  Diaconis conjectured the mixing time of this process to be $O(A^2)$ which we
confirm in this paper. This improves on the currently known $O(\exp(A^2))$
estimate.
