Liouville quantum gravity on the unit disk

Yichao Huang; Rémi Rhodes; Vincent Vargas

doi:10.1214/17-AIHP852

Liouville quantum gravity on the unit disk

Yichao Huang, Rémi Rhodes, Vincent Vargas

Research output: Contribution to journal › Article › peer-review

36 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1694-1730
Number of pages	37
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	54
Issue number	3
DOIs	https://doi.org/10.1214/17-AIHP852
Publication status	Published - Aug 2018
Externally published	Yes

Keywords

Conformal anomaly
Gaussian multiplicative chaos
KPZ formula
KPZ scaling laws
Liouville Quantum Gravity
Polyakov formula
Quantum field theory

Access to Document

10.1214/17-AIHP852

Cite this

@article{ec0c0b775162466e91c7c439933a2e9e,

title = "Liouville quantum gravity on the unit disk",

abstract = "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.",

keywords = "Conformal anomaly, Gaussian multiplicative chaos, KPZ formula, KPZ scaling laws, Liouville Quantum Gravity, Polyakov formula, Quantum field theory",

author = "Yichao Huang and R{\'e}mi Rhodes and Vincent Vargas",

note = "Publisher Copyright: {\textcopyright} Association des Publications de l{\textquoteright}Institut Henri Poincar{\'e}, 2018.",

year = "2018",

month = aug,

doi = "10.1214/17-AIHP852",

language = "English",

volume = "54",

pages = "1694--1730",

journal = "Annales de l'institut Henri Poincare (B) Probability and Statistics",

issn = "0246-0203",

publisher = "Institute of Mathematical Statistics",

number = "3",

}

TY - JOUR

T1 - Liouville quantum gravity on the unit disk

AU - Huang, Yichao

AU - Rhodes, Rémi

AU - Vargas, Vincent

N1 - Publisher Copyright: © Association des Publications de l’Institut Henri Poincaré, 2018.

PY - 2018/8

Y1 - 2018/8

N2 - 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.

AB - 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.

KW - Conformal anomaly

KW - Gaussian multiplicative chaos

KW - KPZ formula

KW - KPZ scaling laws

KW - Liouville Quantum Gravity

KW - Polyakov formula

KW - Quantum field theory

UR - http://www.scopus.com/inward/record.url?scp=85049734159&partnerID=8YFLogxK

U2 - 10.1214/17-AIHP852

DO - 10.1214/17-AIHP852

M3 - Article

AN - SCOPUS:85049734159

SN - 0246-0203

VL - 54

SP - 1694

EP - 1730

JO - Annales de l'institut Henri Poincare (B) Probability and Statistics

JF - Annales de l'institut Henri Poincare (B) Probability and Statistics

IS - 3

ER -

Liouville quantum gravity on the unit disk

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this