Fast ignition of an inertial confinement fusion target by an energetic proton beam is here re-examined. We put special emphasis on the role of the transverse dispersion of the beam induced during its travel between the proton source and the compressed deuterium-tritium (DT) fuel. The theoretical model and the computer code used in our calculations are presented. Different beam initial energy distributions are analyzed. We found that the beam exhibits small collective effects while multiple scattering collisions provide a substantial transverse dispersion of the beam. Therefore, the nuclear dispersion imposes severe restrictions on the schemes for fast ignitor even considering an ideal monoenergetic and noncorrelated proton beam.