I will speak about joint work in progress with Ian Putnam and Karen Strung. The goal of the project is to study the existence of minimal dynamical systems and, more generally, minimal equivalence relations.
In particular, I will discuss the following question: Given a compact Hausdorff space, does there exist a minimal homeomorphism on it? Although the answer is no, a similar question has a positive answer for a finite CW-complex. This question, and the question of which -algebras can be realized as groupoid -algebras, are the motivation for our constructions.
Minimal Dynamical Systems and Groupoids with Prescribed -Theory
Apr. 19, 2018 3pm (MATH 350)
Probability
Manuela Girotti (CSU)
X
We study the distribution of the smallest singular eigenvalues for the finite product of certain random matrix ensemble, in the limit where the size of the matrices becomes large. The limiting distributions that we will study can be expressed as Fredholm determinants of certain integral operators, and generalize in a natural way the extensively studied hard edge Bessel kernel determinant. We will express such quantities in terms of a 2x2 Riemann-Hilbert problem, and use this representation to obtain so-called large gap asymptotics. This is a joint work with Tom Claeys (UC Louvain, Belgium) and Dries Stivigny (KU Leuven, Belgium).
Smallest singular value distribution and large gap asymptotics for products of random matrices