PPT Slide
The number of tracks with N steps that are finishing at coordinate x --> W(N,x) = ?
- possible values of x--> {N, N-2, N-4, ……-(N-2), -N}
- let N+ be the number of steps in + direction; N- the number of steps in - direction
N++N-=N; N+-N-=x; --> we get:
The P(N,x) probability that after N steps the random walker is at coordinate x is:
- Due to the presence of factorials it is hard to work with P(N,x) as given above.
- A more analytical form can be obtained by using the Stirling formula: