We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane C+ associated with the ax + b (affine) group, depending on an admissible Hardy function 0. We obtain the asymptotic behavior of the variance, the exact value of the asymptotic constant, and non-asymptotic upper and lower bounds for the variance on a compact set it C C. As a special case one recovers the DPP related to the weighted Bergman kernel. When iota l iota is chosen within a finite family whose Fourier transform are Laguerre functions, we obtain the DPP associated to hyperbolic Landau levels, the eigenspaces of the finite spectrum of the Maass Laplacian with a magnetic field.
Keywords:
hyperbolic half plane / determinantal point processes / affine group
Source:
Journal of the Mathematical Society of Japan, 2023, 75, 2, 469-483
Funding / projects:
Austrian ministry BMBWF through the WTZ/OeAD-projects [SRB 01/2018, MULT 10/2020]
FWF project 'Operators and Time-Frequency Analysis' [P 31225-N32]
TY - JOUR
AU - Abreu, Luis Daniel
AU - Balazs, Peter
AU - Jakšić, Smiljana
PY - 2023
UR - https://omorika.sfb.bg.ac.rs/handle/123456789/1379
AB - We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane C+ associated with the ax + b (affine) group, depending on an admissible Hardy function 0. We obtain the asymptotic behavior of the variance, the exact value of the asymptotic constant, and non-asymptotic upper and lower bounds for the variance on a compact set it C C. As a special case one recovers the DPP related to the weighted Bergman kernel. When iota l iota is chosen within a finite family whose Fourier transform are Laguerre functions, we obtain the DPP associated to hyperbolic Landau levels, the eigenspaces of the finite spectrum of the Maass Laplacian with a magnetic field.
T2 - Journal of the Mathematical Society of Japan
T1 - The affine ensemble: determinantal point processes associated with the ax plus b group
EP - 483
IS - 2
SP - 469
VL - 75
DO - 10.2969/jmsj/88018801
UR - conv_1708
ER -
@article{
author = "Abreu, Luis Daniel and Balazs, Peter and Jakšić, Smiljana",
year = "2023",
abstract = "We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane C+ associated with the ax + b (affine) group, depending on an admissible Hardy function 0. We obtain the asymptotic behavior of the variance, the exact value of the asymptotic constant, and non-asymptotic upper and lower bounds for the variance on a compact set it C C. As a special case one recovers the DPP related to the weighted Bergman kernel. When iota l iota is chosen within a finite family whose Fourier transform are Laguerre functions, we obtain the DPP associated to hyperbolic Landau levels, the eigenspaces of the finite spectrum of the Maass Laplacian with a magnetic field.",
journal = "Journal of the Mathematical Society of Japan",
title = "The affine ensemble: determinantal point processes associated with the ax plus b group",
pages = "483-469",
number = "2",
volume = "75",
doi = "10.2969/jmsj/88018801",
url = "conv_1708"
}
Abreu, L. D., Balazs, P.,& Jakšić, S.. (2023). The affine ensemble: determinantal point processes associated with the ax plus b group. in Journal of the Mathematical Society of Japan, 75(2), 469-483.
https://doi.org/10.2969/jmsj/88018801
conv_1708
Abreu LD, Balazs P, Jakšić S. The affine ensemble: determinantal point processes associated with the ax plus b group. in Journal of the Mathematical Society of Japan. 2023;75(2):469-483.
doi:10.2969/jmsj/88018801
conv_1708 .
Abreu, Luis Daniel, Balazs, Peter, Jakšić, Smiljana, "The affine ensemble: determinantal point processes associated with the ax plus b group" in Journal of the Mathematical Society of Japan, 75, no. 2 (2023):469-483,
https://doi.org/10.2969/jmsj/88018801 .,
conv_1708 .
