Rigidity of determinantal point processes on the unit disc with sub-Bergman kernels

We give natural constructions of number rigid determinantal point processes on the unit disc D with sub-Bergman kernels of the form K Λ ( z , w ) = ∑ n ∈ Λ ( n + 1 ) z n w ¯ n , z , w ∈ D , with Λ an infinite subset of non-negative integers. Our constructions are given in both deterministic and prob...

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 245; no. 1; pp. 389 - 408
Main Authors Qiu, Yanqi, Wang, Kai
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.10.2021
Springer Nature B.V
Subjects
Algebra
Analysis
Applications of Mathematics
Group Theory and Generalizations
Kernels
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Probabilistic methods
Theoretical
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Summary:We give natural constructions of number rigid determinantal point processes on the unit disc D with sub-Bergman kernels of the form K Λ ( z , w ) = ∑ n ∈ Λ ( n + 1 ) z n w ¯ n , z , w ∈ D , with Λ an infinite subset of non-negative integers. Our constructions are given in both deterministic and probabilistic methods. In the deterministic method, our proofs involve the classical Bloch functions.
ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-021-2219-9