Random Walks fair +1 random walk:flipping a fair coin,the state is the difference between heads and tails; random walk on a graph; card shuffling:random walk in a state space of permutations; random walk on q-coloring of a graph;Random Walks • fair ±1 random walk: flipping a fair coin, the state is the difference between heads and tails; • random walk on a graph; • card shuffling: random walk in a state space of permutations; • random walk on q-coloring of a graph;