On the Mixing Rate of the Triangulation

Let T n denote the set of triangulations of a convex polygon K with n sides. We study the random walk on T n whose transitions are \\ips" of one of the n ? 3 internal diagonals of the current triangulation, the choice of diagonal being random. By bounding the conductance of this graph we show that the walk mixes rapidly, namely in time O(n). A direct argument is given for the fact that the mixing rate is at least (n 3=2).