Rigidity of the $\operatorname{Sine} _{\beta }$ process

Electronic Communications in Probability

Chhaibi Reda¹ 

关键词: the sine$_ eta $ point process;    rigidity of point processes;    random matrices;   

DOI  :  10.1214/18-ECP195

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

We show that the $\operatorname{Sine} _{\beta }$ point process, defined as the scaling limit of the Circular Beta Ensemble when the dimension goes to infinity, and generalizing the determinantal sine-kernel process, is rigid in the sense of Ghosh and Peres: the number of points in a given bounded Borel set $B$ is almost surely equal to a measurable function of the position of the points outside $B$.

【 授权许可】

CC BY