[難題] convergence using markov chain

[littlefive (名偵探毛利小五郎)]

Let n be a prime, and X_i be iid random variables on the set {1,2,... n}.
Let S_k = X_1 + ... + X_k (mod n).
Show that S_k converges in distribution to the uniform distribution on {1...n}
[Hint: Define an appropriate Markov chain.]

我目前的想法 :

- n is a prime => {0,2,...,n-1} is a field

- 定義馬可夫鏈為 S_k 的值 at step k

- iid X_i on {0,... n} => 矩陣每行每列的和都是 1...

不知道這樣是否合理? 請高手指點... ((_ _))

--
※ 發信站: 批踢踢實業坊(ptt.cc) 
◆ From: 65.95.246.76