Liouville quantum gravity on the unit disk

被引：37

作者：

Huang, Yichao ^{[1
]}

Rhodes, Remi ^{[2
]}

Vargas, Vincent ^{[1
]}

机构：

[1] ENS Ulm, DMA, 45 Rue Ulm, F-75005 Paris, France

[2] Univ Paris Est Marne la Vallee, LAMA, Champs Sur Marne, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2018年 / 54卷 / 03期

关键词：

Liouville Quantum Gravity; Quantum field theory; Gaussian multiplicative chaos; KPZ formula; KPZ scaling laws; Polyakov formula; Conformal anomaly; GAUSSIAN MULTIPLICATIVE CHAOS; BROWNIAN-MOTION; FIELD-THEORY; SPHERE; SLE; 2D;

D O I：

10.1214/17-AIHP852

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：

Our purpose is to pursue the rigorous construction of Liouville Quantum Field Theory on Riemann surfaces initiated by F. David, A. Kupiainen and the last two authors in the context of the Riemann sphere and inspired by the 1981 seminal work by Polyakov. In this paper, we investigate the case of simply connected domains with boundary. We also make precise conjectures about the relationship of this theory to scaling limits of random planar maps with boundary conformally embedded onto the disk.

引用

页码：1694 / 1730

页数：37

共 33 条

[1] Tightness of the recentered maximum of log-correlated Gaussian fields [J].