Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Critical Gaussian Multiplicative Chaos: Convergence of the Derivative Martingale

Abstract : 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 show that the limiting measure has no atom. In connection with the derivative martingale, we write explicit conjectures about the glassy phase of log-correlated Gaussian potentials and the relation with the asymptotic expansion of the maximum of log-correlated Gaussian random variables.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [73 references]  Display  Hide  Download
Contributor : Vincent Vargas Connect in order to contact the contributor
Submitted on : Sunday, July 1, 2012 - 7:46:44 PM
Last modification on : Tuesday, January 18, 2022 - 3:24:29 PM
Long-term archiving on: : Thursday, December 15, 2016 - 7:44:36 PM


Files produced by the author(s)


  • HAL Id : hal-00705619, version 2
  • ARXIV : 1206.1671


Bertrand Duplantier, Rémi Rhodes, Scott Sheffield, Vincent Vargas. Critical Gaussian Multiplicative Chaos: Convergence of the Derivative Martingale. 2012. ⟨hal-00705619v2⟩



Record views


Files downloads