The content here is discussed extensively at efavdb.com/random-walk-scaling.
This explains by example what we're talking about below (some statistics around random walks in M dimensions):
Distributions across various M for a couple N:
Gif of distributions and their means:
Static shots of the distributions and their means:
Gif of standard deviations:
and the static figures:
Exponents and scaling factors vs M:
and a log-log for scaling factors of standard deviations vs M:
