PPT Slide

If N>ɭ the important part of P(N,x) is for x<<N.

We use thus the x/N<ə simplification and write:

After neglecting the second order terms in x/N we get:

Which is normalized to 2, on [-?,?]-since it is valid for only each second integer x [otherwise P(N,x)=0]

We can calculate now <x>, and <x2>:

Generalization in 2d and 3d (square and cubic lattice sites)

a random walk of N steps in 2d --> a random walk of N/2 steps along the x axis + a random walk of N/2 steps along the y axis

for 3d in the same manner:

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