## Postdoc Lunch Time Talks

Date: November 8, 2017

Time: 12:00PM - 12:20PM

Location: BLOC 220

Speaker: Rick Lynch, Texas A&M University

Description: Title: Preserving a certain operator property under subgaussian maps

Abstract: In this talk, I will discuss the following result. As long as an operator $\mathbf{D}$ stays bounded away from zero in norm on $S$ and a provided map ${\boldsymbol \Phi}$ comprised of i.i.d. subgaussian rows has number of measurements at least proportional to the square of $w(\mathbf{D}S)$, the Gaussian width of the related set $\mathbf{D}S$, then with high probability the composition ${\boldsymbol \Phi} \mathbf{D}$ also stays bounded away from zero in norm on $S$ with bound proportional to $w(\mathbf{D}S)$. The null space property is preserved w.h.p. under such subgaussian maps as a consequence, and there might be other potential applications in dimension reduction analysis. This is joint work with Peter G. Casazza (University of Missouri) and Xuemei Chen (University of San Francisco).