PERCOLATION OF THE EXCURSION SETS OF PLANAR SYMMETRIC SHOT NOISE FIELDS

Raphaël Lachièze-Rey (1) , Stephen Muirhead (2)

1 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
2 QMUL - Queen Mary University of London

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.

Keywords: sharp phase transition; shot noise fields; excursions; percolation; sharp phase transition

Domains: Probability [math.PR]

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⟩