R.C.
Lua and A.Y. Grosberg, PRE 72, 061918 (2005):
Sub-diffusive dynamics implies long (power-law) tails in
the distribution of first passage times, such that the MFPT is infinite.
This indeed follows from the fractional diffusion equation,
and is also the property of continuous time random walks with
appropriate power-law distribution of waiting times.
However, these simple examples involve uncorrelated steps.
Sub-diffusion due to correlated motions of the many polymeric degrees of
freedom may well be different.
We simulated the sub-diffusive motion of the central monomer
in a one-dimensional phantom polymer. The probability distribution of the
first passage were exponentially distributed in this case.
[Plots corresponding to N=3, 9, 33, 129; the last overlapping
with 513 and 1025 (not shown)]
