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

2017/02/01 by Parthanil Roy, Roy, Parthanil
Mathematics · #37A40 (Secondary) #60G52 #60G60 (Primary) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1702.00393

openalex publication_date 2017/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a self-contained introduction to the applications of ergodic theory\nof nonsingular (also known as quasi-invariant) group actions and the structure\ntheorem for finitely generated abelian groups on the extreme values of\nstationary symmetric stable random fields indexed by \ℤ^d. It is\nbased on a mini course given in the Eighth Lectures on Probability and\nStochastic Processes (held in the Bangalore Centre of Indian Statistical\nInstitute during December 6-10, 2013) except that a few recent references have\nbeen added in the concluding part. This article is a survey of existing work\nand the proofs are therefore skipped or briefly outlined.\n

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