Speaker:
Jorge Garza-Vargas
Speaker Link:
Institution:
UC Berkeley
Time:
Wednesday, April 13, 2022 - 2:00pm to 3:00pm
Location:
510R Rowland Hall
Let Td,N be a random symmetric Wigner-type tensor of dimension N and order d. For unit vectors u(1)N,…,u(d−2)N we study the random matrix obtained by taking the contracted tensor 1NTd,n[u(1)N⊗⋯⊗u(d−2)N] and show that, for large N, its spectral empirical distribution concentrates around a semicircular distribution whose radius is an explicit symmetric function of the uNi. We further generalize this result by then considering a family of contractions of Td,N and show, using free probability concepts, that its joint distribution is well-approximated by a non-commutative semicircular family when N is large. This is joint work with Benson Au (https://arxiv.org/abs/2110.01652).