Question: 6 , at each stage. Show that the probability wn that the particle revisits its starting point at the nth stage is given by w2m+1

6 , at each stage. Show that the probability wn that the particle revisits its starting point at the nth stage is given by w2m+1 = 0, w2m =



1 2

2m 

2m m

 X

(i, j,k): i+j+k=m



m!

3mi ! j ! k!

2

.

180 Random walks Use Stirling’s formula to show that

∞X n=0 wn < ∞.

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