On Gaussian multiplicative chaos

2014/07/16 by Shamov, Alexander · 9 citations
#60B10 (Secondary) #60G15 (Primary) #60G57 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1407.4418

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.

Cited by

• Fourier dimension of imaginary Gaussian multiplicative chaos
• Around the semi-classical limit of boundary Liouville conformal field theory
• Hölder type estimates for Gaussian multiplicative chaos
• Liouville quantum gravity: from random planar maps to conformal field theory
• On the Fourier Coefficients of critical Gaussian multiplicative chaos
• A coupling for the Liouville and the sinh-Gordon model in the L² phase
• Two Decades of Probabilistic Approach to Liouville Conformal Field Theory
• The Liouville model in the L¹ phase: coupling and extreme values
• Conditional GMC within the stochastic heat flow

Related

• Critical Gaussian multiplicative chaos: a review
• Uniqueness of supercritical Gaussian multiplicative chaos
• The uniqueness of the Gaussian multiplicative chaos revisited
• Critical Gaussian Multiplicative Chaos revisited
• Gaussian multiplicative chaos through the lens of the 2D Gaussian free field