An elementary approach to Gaussian multiplicative chaos | Zendy

Nathanaël Berestycki | Zendy

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An elementary approach to Gaussian multiplicative chaos

Author(s) -

Nathanaël Berestycki

Publication year - 2017

Publication title -

electronic communications in probability

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.236

H-Index - 38

ISSN - 1083-589X

DOI - 10.1214/17-ecp58

Subject(s) - mathematics , multiplicative function , limiting , measure (data warehouse) , gaussian , gaussian free field , limit (mathematics) , chaos (operating system) , statistical physics , convergence (economics) , discrete mathematics , mathematical analysis , quantum mechanics , physics , computer security , computer science , mechanical engineering , database , engineering , economics , economic growth

A completely elementary and self-contained proof of convergence of Gaussian multiplicative chaos is given. The argument shows further that the limiting random measure is nontrivial in the entire subcritical phase $(\gamma < \sqrt{2d})$ and that the limit is universal (i.e., the limiting measure is independent of the regularisation of the underlying field)

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