|
1
|
Levi M, Marzo J, Ortega-Cerdà J. Linear Statistics of Determinantal Point Processes and Norm Representations. INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2024; 2024:12869-12903. [DOI: 10.1093/imrn/rnae182] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/05/2025]
Abstract
Abstract
We study the asymptotic behavior of the fluctuations of smooth and rough linear statistics for determinantal point processes on the sphere and on the Euclidean space. The main tool is the generalization of some norm representation results for functions in Sobolev spaces and in the space of functions of bounded variation.
Collapse
Affiliation(s)
- Matteo Levi
- Fac. de Ciències, Universitat Autònoma de Barcelona , 08193 Bellaterra,
- Dept. Matemàtica i Informàtica, Universitat de Barcelona , Gran Via 585, 08007 Barcelona,
| | - Jordi Marzo
- Dept. Matemàtica i Informàtica, Universitat de Barcelona , Gran Via 585, 08007 Barcelona,
- CRM, Centre de Recerca Matemàtica, Campus de Bellaterra Edifici C , 08193 Bellaterra, Barcelona,
| | - Joaquim Ortega-Cerdà
- Dept. Matemàtica i Informàtica, Universitat de Barcelona , Gran Via 585, 08007 Barcelona,
- CRM, Centre de Recerca Matemàtica, Campus de Bellaterra Edifici C , 08193 Bellaterra, Barcelona,
| |
Collapse
|
|
2
|
Barthelmé S, Tremblay N, Usevich K, Amblard PO. Determinantal point processes in the flat limit. BERNOULLI 2023. [DOI: 10.3150/22-bej1486] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/22/2023]
Affiliation(s)
- Simon Barthelmé
- CNRS, Univ. Grenoble Alpes, Grenoble INP, GIPSA-lab, Grenoble, France
| | - Nicolas Tremblay
- CNRS, Univ. Grenoble Alpes, Grenoble INP, GIPSA-lab, Grenoble, France
| | - Konstantin Usevich
- Université de Lorraine and CNRS, CRAN (Centre de Recherche en Automatique en Nancy), Grenoble, France
| | | |
Collapse
|
|
3
|
Tremblay N, Barthelmé S, Usevich K, Amblard PO. Extended L-ensembles: A new representation for determinantal point processes. ANN APPL PROBAB 2023. [DOI: 10.1214/22-aap1824] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/24/2023]
Affiliation(s)
| | | | - Konstantin Usevich
- Université de Lorraine and CNRS, CRAN (Centre de Recherche en Automatique de Nancy)
| | | |
Collapse
|
|
4
|
Poinas A, Lavancier F. Asymptotic approximation of the likelihood of stationary determinantal point processes. Scand Stat Theory Appl 2022. [DOI: 10.1111/sjos.12613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Arnaud Poinas
- Laboratoire de Mathématiques et Applications – UMR 7348 – Poitiers France
| | | |
Collapse
|
|
5
|
Coeurjolly JF, Mazoyer A, Amblard PO. Monte Carlo integration of non-differentiable functions on [0,1]ι, ι=1,…,d, using a single determinantal point pattern defined on [0,1]d. Electron J Stat 2021. [DOI: 10.1214/21-ejs1929] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | - Adrien Mazoyer
- Institut de Mathématiques de Toulouse 118 route de Narbonne F-31062 Toulouse Cedex 9, France
| | | |
Collapse
|