An elementary approach to Gaussian multiplicative chaos

By Nathanaël Berestycki. 2015

252 citations recorded by the source corpus.

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)

Subfields: Condensed Matter Physics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b5c50edeb73706eb9656bd4be53489e0aff38142

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Condensed Matter Physics

1. Christian Webb
2. Eero Saksman
3. J. Junnila

In Mathematical Physics

1. Christian Webb
2. Eero Saksman
3. J. Junnila
4. Jasper A. Vrugt
5. Christophe Andrieu
6. Christian P. Robert
7. Jeffrey S. Rosenthal
8. K. Latuszy'nski

Citations in the corpus

• The Riemann zeta function and Gaussian multiplicative chaos: Statistics on the critical line (2016, background): “We also point out Berestycki’s elegant proof for the existence and uniqueness of subcritical Gaussian multiplicative chaos measures [12].”
• Uniqueness of critical Gaussian chaos (2017, methodology): “Finally, in the paper [5] Berestycki provides an elegant and simple treatment of convolution approximations, again in the subcritical regime.”