Elements of Wigner’s Proof
v Compute E(A2k)11= mean(l2k) = (2k)th moment
v Verify that the semicircle is the only distribution
with these moments
v (A2k)11 = SA1xAxy…AwzAz1 “paths” of length 2k
v Need only count number of special paths of length
2k on k objects  (all other terms 0 or negligible!)
v This is a Catalan Number!