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]
The Brownian loop soup by Gregory F. Lawler and Wendelin Werner. Introduction and section 4
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]
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