An urn model of Diaconis and some generalizations are discussed. A convergence theorem is proved that implies for Diaconis’ model that the empirical distribution of balls in the urn converges with probability one to the uniform distribution.
"An urn model of Diaconis." Ann. Probab. 33 (5) 2036 - 2042, September 2005. https://doi.org/10.1214/009117905000000314