Chen, ZaoliSamorodnitsky, Gennady2018-10-152018-10-152018-10-15https://hdl.handle.net/1813/59211We study the extremes for a class of a symmetric stable random fields with long range dependence. We prove functional extremal theorems both in the space of sup measures and in the space of cadlag functions of several variables. The limits in both types of theorems are of a new kind, and only in a certain range of parameters these limits have the Fr\'echet distribution.en-USrandom fieldextremal limit theoremrandom sup measurerandom closed setlong range dependencestable lawheavy tailstechnical report