Rigidity of determinantal point processes with the Airy, the Bessel and the Gamma kernel

被引：33
|
作者：
Bufetov, Alexander I. [1 ,2 ,3 ,4 ]
机构：
[1] Aix Marseille Univ, CNRS, Cent Marseille, I2M,UMR 7373, Marseille, France
[2] VA Steklov Math Inst, Moscow 117333, Russia
[3] Russian Acad Sci, Inst Informat Transmiss Problems, Moscow, Russia
[4] Natl Res Univ, Higher Sch Econ, Moscow, Russia
来源：
BULLETIN OF MATHEMATICAL SCIENCES | 2016年 / 6卷 / 01期
关键词：
Determinantal point processes; Airy kernel; Bessel kernel; Gamma kernel; Rigidity; LEVEL-SPACING DISTRIBUTIONS; FERMION;
D O I：
10.1007/s13373-015-0080-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A point process is said to be rigid if for any bounded domain in the phase space, the number of particles in the domain is almost surely determined by the restriction of the configuration to the complement of our bounded domain. The main result of this paper is that determinantal point processes with the Airy, the Bessel and the Gamma kernels are rigid. The proof follows the scheme used by Ghosh, Ghosh and Peres: the main step is the construction of a sequence of additive statistics with variance going to zero.
引用
收藏
页码：163 / 172
页数：10
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