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6
Elements of Wigner’s Proof
vCompute E(A2k)11= mean(l2k) = (2k)th moment
vVerify that the semicircle is the only distribution with these moments
v(A2k)11 = SA1xAxy…AwzAz1 “paths” of length 2k
vNeed only count number of special paths of length 2k on k objects  (all other terms 0 or negligible!)
vThis is a Catalan Number!
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