In an infinite cubic lattice with points separated in x, y and z axis by one unit, a random walk starts from (0, 0, 0). Any of the 6 possible directions is equally likely at each step.
What is the probability of a return to the origin after 2*N moves?
(In reply to
expanded table using OEIS by Charlie)
The cumulative probability is actually misleading. A path that returns to the origin more than once is counted each time it returns there, so the shown cumulative probability is larger than the actual probability that a return will have been made at least once.
The overall probability that a random walk will return to the origin in this 3d space at least once is 0.340537.
See A086230.
Edited on July 4, 2024, 11:29 am
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Posted by Charlie
on 2024-07-04 08:26:37 |
re: expanded table using OEIS - a caveat
