AG Mathematische Stochastik : – Neil Manibo

Title: Ghost measures and the finiteness conjecture for matrices

Abstract:

In 1995, Lagarias and Wang asked whether, given a finite set S of real matrices,
there is always a finite product of matrices from S which realises the joint
spectral radius of S. The general conjecture has been shown to be false for real
matrices, but it remains open for matrices with rational/integer entries.
Regular sequences, which are sequences arising from a finite set a matrices, are
intimately related to this question. In this talk, we will discuss how to build
probability measures on [0,1) from regular sequences, and show that for a
specific class of matrices, the finiteness property is equivalent to spectral
properties of the derived measures. This is based on joint work with Michael
Coons, James Evans, and Philipp Gohlke.

https://www.math.fau.de/stochastik/oberseminar-stochastik/