Rescaled weighted determinantal random balls
ESAIM: Probability and Statistics, Tome 24 (2020), pp. 227-243.

We consider a collection of weighted Euclidian random balls in ℝ$$ distributed according a determinantal point process. We perform a zoom-out procedure by shrinking the radii while increasing the number of balls. We observe that the repulsion between the balls is erased and three different regimes are obtained, the same as in the weighted Poissonian case.

Reçu le :
Accepté le :
Première publication :
Publié le :
DOI : 10.1051/ps/2020005
Classification : 60G55, 60F05, 60G60, 60G10, 60G52
Mots-clés : Determinantal point processes, generalized random fields, limit theorem, point processes, stable fields 
@article{PS_2020__24_1_227_0,
     author = {Clarenne, Adrien},
     title = {Rescaled weighted determinantal random balls},
     journal = {ESAIM: Probability and Statistics},
     pages = {227--243},
     publisher = {EDP-Sciences},
     volume = {24},
     year = {2020},
     doi = {10.1051/ps/2020005},
     mrnumber = {4079211},
     zbl = {1447.60076},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps/2020005/}
}
TY  - JOUR
AU  - Clarenne, Adrien
TI  - Rescaled weighted determinantal random balls
JO  - ESAIM: Probability and Statistics
PY  - 2020
SP  - 227
EP  - 243
VL  - 24
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ps/2020005/
DO  - 10.1051/ps/2020005
LA  - en
ID  - PS_2020__24_1_227_0
ER  - 
%0 Journal Article
%A Clarenne, Adrien
%T Rescaled weighted determinantal random balls
%J ESAIM: Probability and Statistics
%D 2020
%P 227-243
%V 24
%I EDP-Sciences
%U http://www.numdam.org/articles/10.1051/ps/2020005/
%R 10.1051/ps/2020005
%G en
%F PS_2020__24_1_227_0
Clarenne, Adrien. Rescaled weighted determinantal random balls. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 227-243. doi : 10.1051/ps/2020005. http://www.numdam.org/articles/10.1051/ps/2020005/

[1] H. Biermé and A. Estrade, Poisson random balls: self similarity and X-ray images. Adv. Appl. Prob. 38 (2006) 1–20. | DOI | MR | Zbl

[2] H. Biermé, A. Estrade and I. Kaj, Self-similar random fields and rescaled random balls models. J. Theoret. Probab. 23 (2010) 1110–1141. | DOI | MR | Zbl

[3] J.-C. Breton and C. Dombry. Rescaled weighted random balls models and stable self-similar random fields. Stoch. Proc. Appl. 119 (2009) 3633–3652. | DOI | MR | Zbl

[4] J.-C. Breton, A. Clarenne and R. Gobard, Macroscopic analysis of determinantal random balls. 25 (2019) 1568–1601. | MR

[5] D.J. Daley and D. Vere-Jones, Introduction to point processes. Volumes 1 and 2, 2nd Ed (2002).

[6] M.A. De Gosson, Symplectic Methods in Harmonic Analysis and in Mathematical Physics, vol. 7 (2011) 185–198. | MR | Zbl

[7] N. Deng, W. Zhou and M. Haenggi, The Ginibre Point Process as a Model for Wireless Networks with Repulsion. Preprint (2014). | arXiv

[8] R. Gobard, Random balls model with dependence. J. Math. Anal. Appl. 423 (2015) 1284–1310. | DOI | MR | Zbl

[9] J.B. Hough, M. Krishnapur, Y. Peres and B. Virág, Zeros of Gaussian Analytic Functions and Determinantal Point Processes. In Vol. 51 of University Lecture series. AMS (2009). | MR | Zbl

[10] I. Kaj, L. Leskelä, I. Norros and V. Schmidt, Scaling limits for random fields with long-range dependence. Ann. Probab. 35 (2007) 528–550. | MR | Zbl

[11] I. Kaj and M.S. Taqqu, Convergence to fractional Brownian motion and to the Telecom process: the integral representation approach. In and out of equilibrium. 2. Progr. Probab. 60 (2008) 383–427. | DOI | MR | Zbl

[12] T. Mikosch, S. Resnick, H. Rootzén and A. Stegeman, Is network traffic approximated by stable Lévy motion of fractional Brownian motion ?. Ann. App. Probab. 12 (2002) 23–68. | MR | Zbl

[13] N. Miyoshi and T. Shirai, A cellular model with Ginibre configured base stations. Adv. Appl. Probab. 46 (2014) 832–845. | DOI | MR | Zbl

[14] G. Samorodnitsky and M. Taqqu, Stable Non-Gaussian Random Processes. Chapman and Hall (1994). | MR | Zbl

[15] X. Yang and A.P. Petropulu, Co-Channel interference modeling in a Poisson field of interferers in wireless communications. IEEE Trans. Signal Process. 51 (2003) 64–76. | DOI | MR | Zbl

Cité par Sources :