Abstract
We study fine properties of the convergence of a high intensity shot noise field towards the Gaussian field with the same covariance structure. In particular we (i) establish a strong invariance principle, i.e. a quantitative coupling between a high intensity shot noise field and the Gaussian limit such that they are uniformly close on large domains with high probability, and (ii) use this to derive an asymptotic expansion for the critical level above which the excursion sets of the shot noise field percolate.
On étudie les propriétés fines de convergence d’un champ shot noise haute fréquence vers le champ gaussien de même structure de covariance. En particulier, on (i) établit un strong invariance principle, i.e. un couplage quantitatif entre un champ shot noise haute fréquence et son champ limite gaussien tel qu’ils soient uniformément proches sur de larges domaines avec grande probabilité, et (ii) on en déduit un développement asymptotique du seuil critique de percolation du champ shot noise.
Funding Statement
The second author was supported by the Australian Research Council (ARC) Discovery Early Career Researcher Award DE200101467.
Acknowledgements
The authors thank Chinmoy Bhattacharjee, Michael Goldman, Martin Huesmann, Manjunath Krishnapur and Felix Otto for helpful discussions on strong invariance principles for Poisson random measures, and Giovanni Peccati for suggesting to extend the strong invariance principle to derivatives of the field.
Citation
Raphaël Lachièze-Rey. Stephen Muirhead. "Asymptotics for the critical level and a strong invariance principle for high intensity shot noise fields." Ann. Inst. H. Poincaré Probab. Statist. 59 (3) 1375 - 1397, August 2023. https://doi.org/10.1214/22-AIHP1303
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