Colloquium / Seminars
Topic：Random Operator Theory: Some Results and More Questions
Speaker：Prof. Xiang Fang
(Department of Mathematics, National Central University)
Date time：March 19, 2019 14:00 - 15:00
Tea Party：March 19, 2019 13:30 (SA205)
Abstract：Abstract. Random Matrix Theory (RMT) has evolved into a remarkably sophisticated subject, yet much less is known for its infinite dimensional counterpart, namely, Random Operator Theory (ROT). Moreover, our knowledge on ROT so far is devoted (almost) exclusively to self-adjoint and unbounded differential operators, such as random Schrodinger operators. A theory for non-selfadjoint and bounded ROT is largely missing so far. This report is on some of our initial efforts to explore this untapped area. In particular, we introduce and study a clearly fundamental yet unexplored model, which we call “random weighted shifts”. Other models, such as random Hardy/Bergman spaces, random Toeplitz operators, random coefficient multipliers, random Carleson measures, etc., are proposed, but we have more questions than answers.
(Joint work with Cheng Guozheng and Zhu Sen.)