【校庆学术报告】Distributional inequalities for noncommutative martingales

Yong Jiao 焦勇  (Central South University)

10:00-11:00, October 28, 2022   Tencent Meeting ID: 140 838 779

Abstract:

We establish distributional estimates for noncommutative martingales, in the sense of decreasing rearrangements of the spectra of unbounded operators, which generalises the study of distributions of random variables. Our results include distributional versions of the noncommutative Stein, dual Doob, martingale transform and Burkholder-Gundy inequalities. Our proof relies upon new and powerful extrapolation theorems. As an application, we obtain some new martingale inequalities in symmetric quasi-Banach operator spaces and some interesting endpoint estimates. Our main approach demonstrates a method to build the noncommutative and classical probabilistic inequalities in an entirely operator theoretic way.

About the speaker:

焦勇, 教授，博士生导师；国家杰出青年基金和国家优秀青年基金获得者；中南大学数学与统计学院院长。主要研究方向：非交换分析；主要成果发表在《Advances in Math》、 《Commun. Math. Phys》、 《International Math. Research Notices》、《Transactions of American Math. Society》、《Annals of Probability》、《JFA》和《Probability Theory and Related Fields》等国内外重要学术期刊上。目前担任教育部第八届科技委数理学部委员、中国工程概率统计学会理事长和湖南省数学会副理事长。

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