• français
    • English
  • English 
    • français
    • English
  • Login
JavaScript is disabled for your browser. Some features of this site may not work without it.
BIRD Home

Browse

This CollectionBy Issue DateAuthorsTitlesSubjectsJournals BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesSubjectsJournals

My Account

Login

Statistics

View Usage Statistics

Critical Gaussian Multiplicative Chaos: Convergence of the Derivative Martingale

Thumbnail
Date
2014
Link to item file
https://arxiv.org/abs/1206.1671v3
Dewey
Probabilités et mathématiques appliquées
Sujet
multiplicative chaos; scale invariance; kpz; star equation; random measure
Journal issue
Annals of Probability
Volume
42
Number
5
Publication date
2014
Article pages
1769-1808
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/13-AOP890
Forthcoming
oui
URI
https://basepub.dauphine.fr/handle/123456789/9720
Collections
  • CEREMADE : Publications
Metadata
Show full item record
Author
Duplantier, Bertrand
Rhodes, Rémi
Sheffield, Scott
Vargas, Vincent
Type
Article accepté pour publication ou publié
Abstract (EN)
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.

  • Accueil Bibliothèque
  • Site de l'Université Paris-Dauphine
  • Contact
SCD Paris Dauphine - Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16

 Content on this site is licensed under a Creative Commons 2.0 France (CC BY-NC-ND 2.0) license.