Density of states in the band tails and random multiplication in a diffusive medium

We have considered the problem of random multiplication of particles or fields in a diffusive medium. Both the short-time and asymptotic behavior is evaluated. We have used already known results on the density of states in disordered systems and on transverse spin depolarization in a medium with random magnetic fields. We have treated both bounded and unbounded random potentials. We reaffirm certain recent results and also point out some differences.