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Gregory F. Lawler studies random walks, Brownian motion and Schramm–Loewner evolution, with connections to statistical physics and complex analysis. His University of Chicago research profile emphasizes paths such as loop-erased random walks and their relation to uniform spanning trees.^[ref]

Lawler and Wendelin Werner developed the Brownian loop soup, using a conformally invariant measure on planar Brownian loops to build a Poisson point process of loops.^[ref] His Notes on the Bessel Process by Gregory F. Lawler provide another route from paths to geometry: a Bessel process describes radial diffusion, with its dimension parameter controlling whether the origin is reached. The boundary behavior matters when extending the process beyond its first zero.^[ref]

By Gregory F. Lawler, Wendelin Werner. Probability Theory and Related Fields 128, 565–588.

Author preprint: arxiv.org/abs/math/0304419

Section 4.1, equation (15), defines loop measure by normalized planar Brownian bridges with density 1/(2 pi t squared); Proposition 6 proves conformal invariance. The introduction defines loop soups as Poisson samples of this measure. The arXiv PDF date displayed by the current rendering is not used as the journal publication date.

Wendelin Werner studies random geometric objects arising in probability theory and statistical physics, especially planar paths and their behavior under conformal maps. His work connects Brownian motion and Schramm–Loewner evolution with the geometry of random curves. His personal page identifies him at the University of Cambridge.^[ref]

With Gregory F. Lawler, Werner constructed the Brownian loop soup from a measure on unrooted planar Brownian loops. Sampling loops by a Poisson point process turns an invariant measure into a random collection of paths. The construction provides a way to add Brownian loops to a simple curve and study conformally invariant random geometry.^[ref]