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Posted 2015-04-20, 12:06 AM in reply to Demosthenes's post starting "I tried using my new expansion for R...."
The integral seems fine for d=1 (both for obvious inputs, like a probability of 1/2 for the point x=1 after one step, and less obvious ones simulated by your program).

For d=2 dimensions, a simple case for which the distribution seems to fail is the point and M=2 steps, which should yield a probability of 1/8 (each walk corresponds to a word of length 2 in the alphabet {U,D,L,R}. There are 16 such words in total, of which only UR and RU correspond to a desired walk). In this case, the integral becomes

for so the product is

Actually, this seems like a pretty fun problem to solve by counting words...
"Stephen Wolfram is the creator of Mathematica and is widely regarded as the most important innovator in scientific and technical computing today." - Stephen Wolfram

Last edited by Chruser; 2015-04-20 at 12:20 AM.
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