CMI Seminar: Eliza O'Reilly
Poisson hyperplane tessellations in high dimensions and one-bit compression
In this talk, we will discuss random tessellations of R^n induced by stationary Poisson hyperplanes as the dimension n tends to infinity. We consider metrics of the cells of the tessellation motivated by the data compression method used in one-bit compressed sensing. That is, assuming data in R^n is compressed using one bit with respect to each hyperplane, it is determined how the intensity of the hyperplanes must scale with n to ensure either sufficient separation of different data or sufficient proximity of data compressed together. This study leads to new insights on the nature of the cells of these tessellations in high dimensions and a connection with random polytopes defined as the convex hull of independent and identically distributed random points. Based on joint work with François Baccelli.