  We investigate the motion of a domain wall in the presence of a dynamical
hyperfine field. At temperature T high compared to the hyperfine coupling, the
nuclear spins create a spatially random potential landscape, with dynamics
dictated by the nuclear relaxation time $T_2$. The distribution of the domain
wall relaxation times (both in the thermal and quantum regimes) can show a long
tail, characteristic of stochastic processes where rare events are important.
Here, these are due to occasional strong fluctuations in the nuclear spin
polarisation.
