Events for 11/08/2022 from all calendars

Student/Postdoc Working Geometry Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Xuehan Hu, TAMU

Title: Small ball probabilities for simple random tensors

Abstract: We study the small ball probability of simple random tensor X = X(1) ⊗ · · · ⊗ X(l) where X(i), 1 ≤ i ≤ l are independent random vectors in $\mathbb R^{n}$ that are log-concave or have density bounded by 1. We show that the probability that the projection of X onto an m-dimensional subspace F falls Within an Euclidean ball of length ε is upper bounded by Cεlog(1/\varepsilon)^{l−1} and ε also this upper bound is sharp when m is small. When the subspace is spanned by orthonormal uniform random vectors on the unit sphere, then we can obtain a much better estimate with high probability in terms of the random subspace.