※ 引述《Leon (Achilles)》之銘言：
: 2. 請問幾步之後他會收斂到 stationary probability?
: Ans: 這問題也是很大, 因為這牽扯到 Markov Chain mixing time,
: 這是 Markov Chain Monte Carlo 的核心問題, 也.. 難解.
: 但是, 求解 stationary probability distribution 的過程,
: 漂亮的令你難以想像.
: We can define the Graph G = (v,e),
: Let node j is the neightbor of node i,
: and we define the number of neighbor for node i as N(i).
: Then the transition probability (i,j) is = 1/N(i),
: if j is the neighbor of i.
: Otherwise, it's 0.
: And, obvious;y, sum of N(i) = 2|e|
: 然後這是我們的 Claim:
: The stationary probability for node i = 1/2|e| * N(i).
: 證明非常的簡單:
: if p is the station probability, then p = M*p, M is the transition.
: Thus, let's consider probability for node i after transition
: It will equal to
: sum_{j in neighbor of i} p(j,i) p(j)
: = sum_{..} 1/N(j) * 1/2|e|* N(j)
: = 1/2|e| sum_{..}* 1
: = 1/2|e| N(i)
: