Given a graph, perform the following randomized coloring procedure to it: pick an edge at random and with probability $p$ color the end vertices of that edge blue; otherwise color them red. Repeat indefinitely, choosing the edges with replacement. This induces a random walk in the space of all red/blue colorings of the graph, which converges to a stationary distribution. In this talk we will study this stationary distribution for the complete graph with the goal of getting Jay a PhD.