  A sorting network is a shortest path from $12\dots n$ to $n\dots 21$ in the
Cayley graph of the symmetric group $\mathfrak S_n$ spanned by adjacent
transpositions. The paper computes the edge local limit of the uniformly random
sorting networks as $n\to\infty$. We find the asymptotic distribution of the
first occurrence of a given swap $(k,k+1)$ and identify it with the law of the
smallest positive eigenvalue of a $2k\times 2k$ aGUE (an aGUE matrix has purely
imaginary Gaussian entries that are independently distributed subject to
skew-symmetry). Next, we give two different formal definitions of a spacing --
the time distance between the occurrence of a given swap $(k,k+1)$ in a
uniformly random sorting network. Two definitions lead to two different
expressions for the asymptotic laws expressed in terms of derivatives of
Fredholm determinants.
