Gaussian free fields for mathematicians

Details Gaussian free fields for mathematicians Gaussian free fields for mathematicians

2003-12-04

arxiv.org/abs/math/0312099v3

Mathematics

Probability

27 pages, 1 figure. Typos fixed. Abstract Wiener space discussion added

Scientific paper

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.

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