Electronic Journal of Probability

Uniqueness of critical Gaussian chaos

Janne Junnila and Eero Saksman

Full-text: Open access

Abstract

We consider Gaussian multiplicative chaos measures defined in a general setting of metric measure spaces. Uniqueness results are obtained, verifying that different sequences of approximating Gaussian fields lead to the same chaos measure. Specialized to Euclidean spaces, our setup covers both the subcritical chaos and the critical chaos, actually extending to all non-atomic Gaussian chaos measures.

Article information

Source
Electron. J. Probab., Volume 22 (2017), paper no. 11, 31 pp.

Dates
Received: 28 April 2016
Accepted: 23 January 2017
First available in Project Euclid: 3 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1486090891

Digital Object Identifier
doi:10.1214/17-EJP28

Mathematical Reviews number (MathSciNet)
MR3613704

Zentralblatt MATH identifier
1357.60040

Subjects
Primary: 60G57: Random measures 60G15: Gaussian processes
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G60: Random fields

Keywords
multiplicative chaos uniqueness critical temperature

Rights
Creative Commons Attribution 4.0 International License.

Citation

Junnila, Janne; Saksman, Eero. Uniqueness of critical Gaussian chaos. Electron. J. Probab. 22 (2017), paper no. 11, 31 pp. doi:10.1214/17-EJP28. https://projecteuclid.org/euclid.ejp/1486090891


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