  We investigate the large deviation behaviour of a point process sequence
based on a stationary symmetric stable non-Gaussian discrete-parameter random
field using the framework of Hult and Samorodnitsky (2010). Depending on the
ergodic theoretic and group theoretic structures of the underlying nonsingular
group action, we observe different large deviation behaviours of this point
process sequence. We use our results to study the large deviations of various
functionals (e.g., partial sum, maxima, etc.) of stationary symmetric stable
fields.
