TIGHTNESS OF LIOUVILLE FIRST PASSAGE PERCOLATION FOR γ ∈ (0,2)

被引：0

作者：

Ding, Jian ^{[1
]}

Dubedat, Julien ^{[2
]}

Dunlap, Alexander ^{[3
,4
]}

Falconet, Hugo ^{[2
]}

机构：

[1] Univ Penn, Wharton Sch, Dept Stat, Philadelphia, PA 19104 USA

[2] Columbia Univ, Dept Math, New York, NY 10027 USA

[3] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[4] NYU, Courant Inst Math Sci, Dept Math, New York, NY 10012 USA

来源：

PUBLICATIONS MATHEMATIQUES DE L IHES | 2020年 / 132卷 / 01期

关键词：

GAUSSIAN MULTIPLICATIVE CHAOS; SCALING LIMITS; 1ST-PASSAGE PERCOLATION; PLANAR MAPS; CONVERGENCE; GEODESICS; EXPONENT; MAXIMUM; LAW;

D O I：

10.1007/s10240-020-00121-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study Liouville first passage percolation metrics associated to a Gaussian free field h mollified by the twodimensional heat kernel p(t) in the bulk, and related star-scale invariant metrics. For gamma is an element of(0, 2) and xi = gamma/d gamma, where d(gamma) is the Liouville quantum gravity dimension defined in Ding and Gwynne (Commun. Math. Phys. 374:1877-1934, 2020), we show that renormalized metrics (lambda(-1)(t) e(xi pt)*(h)ds)(t is an element of)(0,1) are tight with respect to the uniform topology. We also show that subsequential limits are bi-Holder with respect to the Euclidean metric, obtain tail estimates for side-to-side distances, and derive error bounds for the normalizing constants lambda(t).

引用

页码：353 / 403

页数：51

共 50 条

[1] Tightness of supercritical Liouville first passage percolation
Ding, Jian
Gwynne, Ewain
[J]. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2023, 25 (10) : 3833 - 3911
[2] Tightness of Liouville first passage percolation for γ∈(0,2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\gamma \in (0,2)$\end{document}
Jian Ding
Julien Dubédat
Alexander Dunlap
Hugo Falconet
[J]. Publications mathématiques de l'IHÉS, 2020, 132 (1) : 353 - 403
[3] The distance exponent for Liouville first passage percolation is positive
Ding, Jian
Gwynne, Ewain
Sepulveda, Avelio
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2021, 181 (04) : 1035 - 1051
[4] Weak LQG metrics and Liouville first passage percolation
Julien Dubédat
Hugo Falconet
Ewain Gwynne
Joshua Pfeffer
Xin Sun
[J]. Probability Theory and Related Fields, 2020, 178 : 369 - 436
[5] The distance exponent for Liouville first passage percolation is positive
Jian Ding
Ewain Gwynne
Avelio Sepúlveda
[J]. Probability Theory and Related Fields, 2021, 181 : 1035 - 1051
[6] Comparison of discrete and continuum Liouville first passage percolation
Ang, Morris
[J]. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2019, 24
[7] Weak LQG metrics and Liouville first passage percolation
Dubedat, Julien
Falconet, Hugo
Gwynne, Ewain
Pfeffer, Joshua
Sun, Xin
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2020, 178 (1-2) : 369 - 436
[8] Tightness of Fluctuations of First Passage Percolation on Some Large Graphs
Benjamini, Itai
Zeitouni, Ofer
[J]. GEOMETRIC ASPECTS OF FUNCTIONAL ANALYSIS: ISRAEL SEMINAR 2006-2010, 2012, 2050 : 127 - 132
[9] (0,2) CHIRAL LIOUVILLE FIELD THEORY
Nakayama, Yu
[J]. MODERN PHYSICS LETTERS A, 2013, 28 (38)
[10] Bounds for distances and geodesic dimension in Liouville first passage percolation
Gwynne, Ewain
Pfeffer, Joshua
[J]. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2019, 24

← 1 2 3 4 5 →