  The local spectral statistics of random matrices forms distinct universality
classes, strongly depending on the position in the spectrum. Surprisingly, the
spacing between consecutive eigenvalues at the spectral edges has received
little attention, where the density diverges or vanishes, respectively. This
different behaviour is called hard or soft edge. We show that the spacings at
the edges are almost indistinguishable from the spacing in the bulk of the
spectrum. We present analytical results for consecutive spacings between the
$k$th and $(k+1)$st smallest eigenvalues in the chiral Gaussian unitary
ensemble, both for finite- and large-$n$. The result depends on the number of
the generic zero modes $\nu$ and the number of flavours $N_{\rm f}$, which are
given in terms of characteristic polynomials, as motivated by Quantum
Chromodynamics (QCD). We find that the convergence in $n$ is very rapid. The
same can be said separately about the limit $k\to\infty$ (limit to the bulk)
and $\nu\to\infty$ (limit to the soft edge). Interestingly, the Wigner surmise
is a very good approximation for all these cases and, apart from $k=1$, shows a
deviation below one percent. These findings are corroborated with Monte-Carlo
simulations. We finally compare for $k=1$ with data from QCD on the lattice,
being in this symmetry class.
