f*******d
发帖数: 339 | 1 For random walk,
L~t
A^2 ~ t,
so L ~ A^2, independent of dimension. | i*****u
发帖数: 26 | 2 Of course N~A^2 is not correct (I have tested for 1D case). The key point is
how the average repeat times at each trajectory depends on L, if the
relation is like: repeat times~A^b then your conclusion will not hold.
This problem is actually pretty difficult, you can make a search to see if it
is already solved by those statistics professionals but I think the
possibility is not high (they are not so interested in the lattice).
I suggest you first have a look on 1D case. This case is very simple | f*******d
发帖数: 339 | 3 You are talking about random walk, not self-avoiding random walk, which is
completely different. For SAW, A~t^0.6 for d=3, but in general
A~ t^m,
m=1 for d=1,
m=3/4 for d=2
m=3/5 for d=3
m=1/2 for d>=4,
For random walk, my congjecture works in 1d, and if your
claim on 2d is correct, then it is also right on 2d, because on 2d N~A^2
according
my conjecture. I admit I don't have any proof, so it may well be wrong,
but alas, you have not proved the trajectory is a fractal.
then
体
point
if
and |
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