Spectral asymptotics for contracted tensor ensembles
Spectral asymptotics for contracted tensor ensembles
Let Td,N:Ω→RNd be a random real symmetric Wigner-type tensor. For unit vectors (uN(i,j))i∈I,j∈[d−2]⊂SN−1, we study the contracted tensor ensemble 1 NTd,NuN(i,1)⊗⋯⊗u N(i,d−2)i∈I. For large N, we show that the joint spectral distribution of this ensemble is well-approximated by a semicircular family (si)i∈I whose covariance (Ki,i′(N))i,i′∈I is given by the rescaled …