We plot in Fig. A1
P( > xgap) for several N values.
We see that, for N = 100 and
xgap = 0.06,
P( > 0.06) 20
per cent. This means that the
probability of finding a gap with a size
larger than six times the mean separation is not significantly small.
When the mean number of lines is large,
λ∼N > > 1, our
P( > xgap) approaches the result obtained by Ostriker et al. (1988)
for small (but still very large if measured in units of the mean separation)
xgap, i.e.,
P( > xgap)∼N(1 - xgap)N-1∼Nexp(- λxgap).