Probability Surveys

The geometry of Brownian surfaces

Rémi Léandre

Full-text: Open access

Abstract

Motivated by Segal’s axiom of conformal field theory, we do a survey on geometrical random fields. We do a history of continuous random fields in order to arrive at a field theoretical analog of Klauder’s quantization in Hamiltonian quantum mechanic by using infinite dimensional Airault-Malliavin Brownian motion.

Article information

Source
Probab. Surveys, Volume 3 (2006), 37-88.

Dates
First available in Project Euclid: 19 April 2006

Permanent link to this document
https://projecteuclid.org/euclid.ps/1145452120

Digital Object Identifier
doi:10.1214/154957806000000032

Mathematical Reviews number (MathSciNet)
MR2216962

Zentralblatt MATH identifier
1189.60104

Subjects
Primary: 60G60: Random fields
Secondary: 81T40: Two-dimensional field theories, conformal field theories, etc.

Keywords
Segal’s axiom Airault-Malliavin equation

Citation

Léandre, Rémi. The geometry of Brownian surfaces. Probab. Surveys 3 (2006), 37--88. doi:10.1214/154957806000000032. https://projecteuclid.org/euclid.ps/1145452120


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