Gaussian free fields for mathematicians

被引：264

作者：

Sheffield, Scott ^{[1
]}

机构：

[1] NYU, Courant Inst, New York, NY 10012 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2007年 / 139卷 / 3-4期

关键词：

D O I：

10.1007/s00440-006-0050-1

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 d-dimensional Gaussian free field (GFF), also called the (Euclidean bosonic) massless free field, is a d-dimensional-time analog of Brownian motion. Just as Brownian motion is the limit of the simple random walk (when time and space are appropriately scaled), the GFF is the limit of many incrementally varying random functions on d-dimensional grids. We present an overview of the GFF and some of the properties that are useful in light of recent connections between the GFF and the Schramm-Loewner evolution.

引用

页码：521 / 541

页数：21

共 24 条

[1]

Adams R., 1975, PURE APPL MATH, V65

[2]

[Anonymous], CONTRIBUTIONS PROB 1

[3]

[Anonymous], 1992, RANDOM WALKS CRITICA, DOI DOI 10.1007/978-3-662-02866-7

[4] Absence of a wetting transition for a pinned harmonic crystal in dimensions three and larger [J].

Bolthausen, E ;

Deuschel, JD ;

Zeitouni, O .

JOURNAL OF MATHEMATICAL PHYSICS, 2000, 41 (03) :1211-1223

[5] Harmonic crystal on the wall: A microscopic approach [J].

Bolthausen, E ;

Ioffe, D .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 187 (03) :523-566

[6]

Bolthausen E, 2001, ANN PROBAB, V29, P1670

[7]

Cardy J.L., 1988, CONFORMAL INVARIANCE, P169

[8]

Di Francesco P., 1997, GRADUATE TEXTS CONT

[9]

Durrett R, 1996, PROBABILITY THEORY E

[10] POLYNOMIALS OF THE OCCUPATION FIELD AND RELATED RANDOM-FIELDS [J].

DYNKIN, EB .

JOURNAL OF FUNCTIONAL ANALYSIS, 1984, 58 (01) :20-52

← 1 2 3 →