  We consider a non relativistic particle on the surface of a semi-infinite
cylinder of circumference $L$ submitted to a perpendicular magnetic field of
strength $B$ and to the potential of impurities of maximal amplitude $w$. This
model is of importance in the context of the integer quantum Hall effect. In
the regime of strong magnetic field or weak disorder $B>>w$ it is known that
there are chiral edge states, which are localised within a few magnetic lengths
close to, and extended along the boundary of the cylinder, and whose energy
levels lie in the gaps of the bulk system. These energy levels have a spectral
flow, uniform in $L$, as a function of a magnetic flux which threads the
cylinder along its axis. Through a detailed study of this spectral flow we
prove that the spacing between two consecutive levels of edge states is bounded
below by $2\pi\alpha L^{-1}$ with $\alpha>0$, independent of $L$, and of the
configuration of impurities. This implies that the level repulsion of the
chiral edge states is much stronger than that of extended states in the usual
Anderson model and their statistics cannot obey one of the Gaussian ensembles.
Our analysis uses the notion of relative index between two projections and
indicates that the level repulsion is connected to topological aspects of
quantum Hall systems.
