Critical Gaussian multiplicative chaos: Convergence of the derivative martingale

In this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching random walks, converges almost surely (in all dimensions) to a random measure with full support. We also...

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Bibliographic Details
Main Authors: Duplantier, Bertrand, Rhodes, Rémi, Vargas, Vincent, Sheffield, Scott Roger
Other Authors: Massachusetts Institute of Technology. Department of Mathematics
Format: Article
Published: Institute of Mathematical Statistics 2018
Online Access:http://hdl.handle.net/1721.1/115337
https://orcid.org/0000-0002-5951-4933