On Gaussian multiplicative chaos

2014/07/16 by Alexander Shamov, Shamov, Alexander · 11 citations
Mathematics · #60B10 (Secondary) #60G15 (Primary) #60G57 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60B10 #msc:60G15 #msc:60G57

paper · pdf · doi:10.48550/arxiv.1407.4418

34 pages. Major revision of the original version. Numeration has changed significantly

arxiv created 2016/05/27 · arxiv updated 2016/05/30

Abstract

We propose a new definition of the Gaussian multiplicative chaos (GMC) and an approach based on the relation of subcritical GMC to randomized shifts of a Gaussian measure. Using this relation we prove general uniqueness and convergence results for subcritical GMC that hold for Gaussian fields with arbitrary covariance kernels.

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