Random Matrix Products and Anderson Localization (19w5086)


(University of California Irvine)

David Damanik (Rice University)


The Banff International Research Station will host the "Random Matrix Products and Anderson Localization" workshop in Banff from September 15, 2019 to September 20, 2019.

In condensed matter physics, Anderson localization is the absence of diffusion of waves in a random (disordered) medium. A popular, though not quite equivalent, mathematical justification of (spectral) Anderson localization is pure point spectrum of the corresponding Schrödinger operator with random potential, along with exponentially decaying eigenfunctions.

The theory of random matrix products goes back to the result by Fürstenberg and Kesten on existence of Lyapunov exponents, and the result of Fürstenberg on the positivity of Lyapunov exponents for random matrix products. Since then enormous amount of attention has been paid to this subject, and currently it has developed into a vast theory of random walks on groups.

While the strong relation between Anderson localization and properties of random matrix products is known, it is far from being completely understood. People working in these areas have quite different backgrounds, and in a sense ``speak different languages''. The purpose of the meeting is to bring together people from spectral theory, dynamical systems, and probability theory that work independently on closely related questions to exchange the ideas and facilitate the collaboration.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).