Maxima of stable random fields,nonsingular actions and finitely generated abelian groups: A survey

This is a self-contained introduction to the applications of ergodic theory of nonsingular (also known as quasi-invariant) group actions and the structure theorem for finitely generated abelian groups on the extreme values of stationary symmetric stable random fields indexed by ? ^d . It is based on a mini course given in the http://www.isid.ac.in/ lps16/PastWebsites/LPS8/index.html Eighth Lectures on Probability and Stochastic Processes (held in the Bangalore Centre of Indian Statistical Institute during December 6–10, 2013) except that a few recent references have been added in the concluding part. This article is a survey of existing work and the proofs are therefore skipped or briefly outlined.