Year: 2025
Type: article
Abstract: Let $\Lambda _\phi $ denote the determinantal point processes associated with the generalized Fock space defined by a doubling subharmonic weight $\phi $. We provide a characterization of the weights $\phi $ such that the process $\Lambda _\phi $ forms a separated sequence in $\mathbb{C}$ almost surely. Furthermore, we emphasize the role of intrinsic repulsion in determinantal processes by comparing $\Lambda _\phi $ with the Poisson process of the same first intensity. As an application, we show that the determinantal process $\Lambda _\alpha $ associated with the canonical weight $\phi _\alpha (z)=|z|^\alpha $, $\alpha>0$, is almost surely separated if and only if $\alpha <4/3$. In contrast, the Poisson process $\Lambda _\alpha ^{P}$ having the same first intensity as $\Lambda _\alpha $ is almost surely separated if and only if $\alpha <1$.
DOI: 10.1093/imrn/rnaf378
Authors: Giuseppe Lamberti, Xavier Massaneda
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7118253777