Uniqueness of critical Gaussian chaos

Janne Junnila; Eero Saksman

doi:10.1214/17-EJP28

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Home > Journals > Electron. J. Probab. > Volume 22 > Article

2017 Uniqueness of critical Gaussian chaos

Janne Junnila, Eero Saksman

Electron. J. Probab. 22: 1-31 (2017). DOI: 10.1214/17-EJP28

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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.