  We study various geometrical aspects of the propagation of particles obeying
fractional statistics in the physical setting of the quantum Hall system. We
find a discrete set of zeros for the two-particle kernel in the lowest Landau
level; these arise from a combination of a two-particle Aharonov-Bohm effect
and the exchange phase related to fractional statistics. The kernel also shows
short distance exclusion statistics, for instance, in a power law behavior as a
function of initial and final positions of the particles. We employ the
one-particle kernel to compute impurity-mediated tunneling amplitudes between
different edges of a finite-sized quantum Hall system and and find that they
vanishes for certain strengths and locations of the impurity scattering
potentials. We show that even in the absence of scattering, the correlation
functions between different edges exhibits unusual features for a narrow enough
Hall bar.
