Speaker: 

Jorge Garza-Vargas

Institution: 

UC Berkeley

Time: 

Wednesday, April 13, 2022 - 2:00pm to 3:00pm

Location: 

510R Rowland Hall

Let $T_{d, N}$ be a random symmetric Wigner-type tensor of dimension $N$ and order $d$. For unit vectors $u_N^{(1)}, \dots, u_{N}^{(d-2)}$ we study the random matrix obtained by taking the contracted tensor $\frac{1}{N} T_{d, n} \left[u_N^{(1)}\otimes \cdots \otimes u_N^{(d-2)} \right]$ and show that, for large $N$, its spectral empirical distribution concentrates around a semicircular distribution whose radius is an explicit symmetric function of the $u_i^N$. We further generalize this result by then considering a family of contractions of $T_{d, N}$ 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).