The d-dimensional Gaussian free field (GFF), also called the (Euclideanbosonic) massless free field, is a d-dimensional-time analog of Brownianmotion. Just as Brownian motion is the limit of the simple random walk (whentime and space are appropriately scaled), the GFF is the limit of manyincrementally varying random functions on d-dimensional grids. We present anoverview of the GFF and some of the properties that are useful in light ofrecent connections between the GFF and the Schramm-Loewner evolution.
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