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]
The Brownian loop soup by Gregory F. Lawler and Wendelin Werner. Introduction and section 4, Brownian loop measure and loop-soup construction
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Wendelin Werner is a prominent French mathematician known for his contributions to probability theory, particularly in the areas of statistical physics, conformal fields, and complex analysis. He was awarded the Fields Medal in 2006, one of the highest honors in mathematics, for his work on random processes and their connections to two-dimensional conformal field theory and statistical mechanics. Werner's research often involves the study of random walks, Brownian motion, and various other stochastic processes.