Percolation of the excursion sets of planar symmetric shot noise fields

Raphael Lachieze-Rey and Stephen Muirhead

Stochastic Processes and their Applications, 2022, vol. 147, issue C, 175-209

Abstract: 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: Percolation; Excursion sets; Shot noise fields; Phase transition (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.01.013

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