Equivalence of Palm measures for determinantal point processes governed by Bergman kernels

被引：4

作者：

Bufetov, Alexander I. ^{[1
,2
,3
,4
,5
]}

Fan, Shilei ^{[1
,6
]}

Qiu, Yanqi ^{[7
,8
]}

机构：

[1] Aix Marseille Univ, CNRS, UMR 7373, Cent Marseille,Inst Math Marseille, 39 Rue F Joliot Curie, F-13453 Marseille, France

[2] RAS, Steklov Math Inst, Moscow, Russia

[3] Inst Informat Transmiss Problems, Moscow, Russia

[4] Natl Res Univ, Higher Sch Econ, Moscow, Russia

[5] St Petersburg State Univ, Chebyshev Lab, St Petersburg, Russia

[6] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China

[7] Univ Paul Sabatier, Inst Math Toulouse, CNRS, 118 Route Narbonne, F-31062 Toulouse 9, France

[8] Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100190, Peoples R China

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2018年 / 172卷 / 1-2期

基金：

欧洲研究理事会;

关键词：

Bergman kernel; Determinantal point process; Conditional measure; Deletion and insertion tolerance; Palm equivalence; Monotone coupling; ERGODIC DECOMPOSITION; FERMION;

D O I：

10.1007/s00440-017-0803-z

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

For a determinantal point process induced by the reproducing kernel of the weighted Bergman space A2(U,.) over a domain U. Cd, we establish the mutual absolute continuity of reduced Palm measures of any order provided that the domain U contains a non-constant bounded holomorphic function. The result holds in all dimensions. The argument uses the H 8 (U)-module structure of A2(U,.). A corollary is the quasi-invariance of our determinantal point process under the natural action of the group of compactly supported diffeomorphisms of U.

引用

页码：31 / 69

页数：39

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