More information on the random walk needed.Does anybody know why that would be? The probability is for a particle arriving at point m on a number line after n moves.
In the case of 0,1 steps with propabilities 1/2, 1/2 the distribution of distance from start after n steps is ~Binomial(1/2,n),
This is the sum of n RV's each with known mean and variance, and the central limit theorem then gives the asymtotic distribution of distance as normal with appropriate mean and variance. This is a Bernoulli process with p=1/2.