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Article Dans Une Revue Stochastic Processes and their Applications Année : 2022

PERCOLATION OF THE EXCURSION SETS OF PLANAR SYMMETRIC SHOT NOISE FIELDS

Résumé

We prove the existence of phase transitions in the global connectivity of the excursion sets of planar symmetric shot noise fields. Our main result establishes a phase transition with respect to the level for shot noise fields with symmetric log-concave mark distributions, including Gaussian, uniform, and Laplace marks, and kernels that are positive, symmetric, and have sufficient tail decay. Without the log-concavity assumption we prove a phase transition with respect to the intensity of positive marks.
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Dates et versions

hal-02337951 , version 1 (29-10-2019)
hal-02337951 , version 2 (20-04-2021)
hal-02337951 , version 3 (24-01-2022)

Identifiants

Citer

Raphaël Lachièze-Rey, Stephen Muirhead. PERCOLATION OF THE EXCURSION SETS OF PLANAR SYMMETRIC SHOT NOISE FIELDS. Stochastic Processes and their Applications, 2022, 147, pp.175-209. ⟨10.1016/j.spa.2022.01.013⟩. ⟨hal-02337951v3⟩
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