I don't have the answer but I figured I would give you the results of a few quick experiments. Here is what things look like when $n = 5$
and when $n = 10$
and when $n = 50$
and when $n = 1000$
The colour represents the probability, red being large, blue being small. The actual colours are assigned according to the log of the probability. To generate these I used the following matlab
M = [ 0 1/5 0; 1/5 1/5 1/5; 0 1/5 0 ]; B = ; n = 50; for i = 1:n B = conv2(B,M); end colormap(jet(256)); imagesc([-n, n], [-n, n], log(B));
Provided that the `shape' close to the origin becomes sufficiently circular, then the answer to your question is positive.