Project Grant 2247966

The National Science Foundation awarded a $466,463 Project Grant to the University of California Irvine under the Mathematical and Physical Sciences program (CFDA 47.049). The grant supports research into non-stationary random dynamical systems and their applications from June 2023 through May 2026.

Key areas of focus include proving that smooth random dynamical systems under an assumption of absence of invariant measures must lead to almost sure exponential growth of norms of random compositions, even in non-stationary cases. The grant will also fund work developing a non-stationary version of the Furstenberg theorem on random matrix products and extending non-commutative versions of the central limit theorem and iterated logarithm law to non-stationary settings for random matrix products and random walks on Lie groups. A third thrust involves proving spectral and dynamical localization for the non-stationary Anderson model, including questions on the topological structure of the spectrum and essential spectrum. Mentoring students is also part of the project scope.