  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.
