Kernels of conditional determinantal measures and the Lyons-Peres completeness conjecture

doi:10.4171/JEMS/1038

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	Kernels of conditional determinantal measures and the Lyons-Peres completeness conjecture
	Bufetov, Alexander, I 1,2,3,4; Qiu, Yanqi 5,6,7; Shamov, Alexander 8
	2021
发表期刊	JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
ISSN	1435-9855
卷号	23 期号:5 页码:1477-1519
摘要	The main result of this paper, Theorem 1.4, establishes a conjecture of Lyons and Peres: for a determinantal point process governed by a self-adjoint reproducing kernel, the system of kernels sampled at the points of a random configuration is complete in the range of the kernel. A key step in the proof, Lemma 1 9, states that conditioning on the configuration in a subset preserves the determinantal property, and the main Lemma 1 10 is a new local property for kernels of conditional point processes. In Theorem 1.6 we prove the triviality of the tail sigma-algebra for determinantal point processes governed by self-adjoint kernels.
关键词	Determinantal point processes Lyons-Peres completeness conjecture conditional measures tail triviality measure-valued martingales operator-valued martingales
DOI	10.4171/JEMS/1038
收录类别	SCI
语种	英语
资助项目	European Research Council (ERC) under the European Union[647133] ; Gabriel Lame Chair at the Chebyshev Laboratory of the SPbSU, a joint initiative of the French Embassy in the Russian Federation ; Saint-Petersburg State University ; IDEX - Programme Investissements d'Avenir of the Government of the French Republic[UNITI -ANR-11-IDEX-0002-02] ; NSF of China[NSFC Y7116335K1] ; NSF of China[NSFC 11801547] ; NSF of China[NSFC 11688101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000658576400006
出版者	EUROPEAN MATHEMATICAL SOC-EMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58795
专题	中国科学院数学与系统科学研究院
通讯作者	Bufetov, Alexander, I
作者单位	1.Aix Marseille Univ, Cent Marseille, CNRS, Inst Math Marseille,UMR7373, F-13453 Marseille, France 2.RAS, Steklov Math Inst, Moscow, Russia 3.Inst Informat Transmiss Problems, Moscow, Russia 4.St Petersburg State Univ, Chebyshev Lab, St Petersburg, Russia 5.Chinese Acad Sci, Inst Math, AMSS, Beijing, Peoples R China 6.Hua Loo Keng Key Lab Math, Beijing, Peoples R China 7.Univ Paul Sabatier, Inst Math Toulouse, CNRS, Toulouse, France 8.Weizmann Inst Sci, Dept Math, Rehovot, Israel
推荐引用方式 GB/T 7714	Bufetov, Alexander, I,Qiu, Yanqi,Shamov, Alexander. Kernels of conditional determinantal measures and the Lyons-Peres completeness conjecture[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY,2021,23(5):1477-1519.
APA	Bufetov, Alexander, I,Qiu, Yanqi,&Shamov, Alexander.(2021).Kernels of conditional determinantal measures and the Lyons-Peres completeness conjecture.JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY,23(5),1477-1519.
MLA	Bufetov, Alexander, I,et al."Kernels of conditional determinantal measures and the Lyons-Peres completeness conjecture".JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY 23.5(2021):1477-1519.