Abstract
Universality laws in geometric random matrix theory
Joel Tropp
California Institute of Technology
A basic problem in geometry is to understand the probability that a uniformly random subspace of a given codimension intersects a fixed convex set. The hitting probability exhibits a phase transition as the codimension of the subspace increases. That is, the probability changes rapidly from one to zero when the codimension reaches the "statistical dimension," a geometric invariant of the convex set.
The focus of this talk is a new universality law in random matrix theory connected to this geometric problem. For a fixed convex set, the location of the phase transition is *universal* over a large class of random subspaces that are constructed as the kernels of random matrices.
On joint works with Dennis Amelunxen, Martin Lotz, Michael McCoy, and Samet Oymak.
The focus of this talk is a new universality law in random matrix theory connected to this geometric problem. For a fixed convex set, the location of the phase transition is *universal* over a large class of random subspaces that are constructed as the kernels of random matrices.
On joint works with Dennis Amelunxen, Martin Lotz, Michael McCoy, and Samet Oymak.
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