Gaussian Multiplicative Chaos Through the Lens of the 2D Gaussian Free Field

被引：0
作者：
Aru, Juhan [1 ]
机构：
[1] Ecole Polytech Fed Lausanne, Inst Math, CH-1015 Lausanne, Switzerland
来源：
MARKOV PROCESSES AND RELATED FIELDS | 2020年 / 26卷 / 01期
关键词：
Gaussian multiplicative chaos; Gaussian free field; Lionville measure; KPZ relation; QUANTUM-GRAVITY;
D O I：
暂无
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
The aim of this review-style paper is to provide a concise, self-contained and unified presentation of the construction and main properties of Gaussian multiplicative chaos (GMC) measures for log-correlated fields in 2D in the subcritical regime. By considering the case of the 2D Gaussian free field, we review convergence, uniqueness and characterisations of the measures; revisit Kahane's convexity inequalities and existence and scaling of moments; discuss the measurability of the underlying field with respect to the GMC measure and present a KPZ relation for scaling exponents.
引用
收藏
页码：17 / 56
页数：40
相关论文
共 25 条
  • [1] Adler J., 1990, LECT NOTES MONOGRAPH, V12, pi
  • [2] [Anonymous], ARXIV170105872
  • [3] [Anonymous], 2016, ARXIV160207323
  • [4] Random conformal weldings
    Astala, Kari
    Jones, Peter
    Kupiainen, Antti
    Saksman, Eero
    [J]. ACTA MATHEMATICA, 2011, 207 (02) : 203 - 254
  • [5] Barral J, 2004, P SYMP PURE MATH, V72, P53
  • [6] BERESTYCKI N, 2015, LECT NOTES
  • [7] Berestycki N., 2014, ARXIV14105407
  • [8] An elementary approach to Gaussian multiplicative chaos
    Berestycki, Nathanael
    [J]. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2017, 22
  • [9] Liouville Quantum Gravity on the Riemann Sphere
    David, Francois
    Kupiainen, Antti
    Rhodes, Remi
    Vargas, Vincent
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2016, 342 (03) : 869 - 907
  • [10] Duplantier B., 2021, ASTERISQUE
123