Quasi-symmetries and rigidity for determinantal point processes associated with de Branges spaces. (English) Zbl 1371.60086

Summary: In this note, we show that determinantal point processes on the real line corresponding to de Branges spaces of entire functions are rigid in the sense of Ghosh-Peres and, under certain additional assumptions, quasi-invariant under the group of diffeomorphisms of the line with compact support.


60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60B20 Random matrices (probabilistic aspects)
46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
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